(CNN) -- In his first visit to Israel and the West Bank since assuming the White House, President Barack Obama ventures into a region of the world whose politics are layered and complex.
As he meets with Israeli Prime Minister Benjamin Netanyahu, Obama will address problems on many levels, including his chilly relationship with Netanyahu, Iran's growing nuclear threat, Syria's possible use of chemical arms and the elusive prospect of peace between Israel and the Palestinians.
The to-do list is ambitious. Obama isn't expected to unveil a major peace plan, but the four-day visit will help define the two-term president's legacy in the Mideast.
1. Repairing personal politics
Netanyahu and Obama sometimes have been at odds.
Netanyahu was perceived by the Israeli left as supporting Obama's opponent, Mitt Romney, in last fall's election. Netanyahu's administration also was perceived as slighting the Obama administration when Israel issued permits for settlement building while Vice President Joe Biden was visiting in 2010.
For Obama's part, an open mike in 2011 caught his complaining about having to deal with Netanyahu, and Obama didn't meet with the Israeli leader when he visited the United States last fall. Obama cited a scheduling conflict.
At the opening news conference Wednesday, both men were demonstrably friendly in exchanging handshakes.
2. Iran's nuclear program
Netanyahu pressed Obama last year to draw a red line on Iran's expanding nuclear program.
Obama indicates he has wiggle room before Iran's nuclear capacity crosses a line, and he is expected to urge Israel to give diplomacy more time. While open to that idea, Netanyahu adds that diplomacy has yet to deter Iran and will press Obama on committing to military options against Iran.
Obama said Wednesday there was still time for a diplomatic resolution to the situation, but added that each country has to make "the awesome decision to engage in any kind of military action" for itself.
3. Syrian civil war
As Obama began the trip in Israel, he reiterated his warning to Syria's government that it would be held accountable for the use of chemical weapons "or their transfer to terrorists."
The warning comes amid allegations by the Syrian President Bashar al-Assad's government and rebels that each used chemical weapons in recent fighting.
"We intend to investigate thoroughly exactly what happened," Obama told reporters Wednesday during a joint news conference in Jerusalem with Netanyahu.
The president said he was "deeply skeptical" of Syrian government claims that the opposition had used chemical weapons.
Obama has previously said Syria's use of chemical weapons would cross a "red line."
"We have been very clear to the Assad regime -- but also to other players on the ground -- that a red line for us is, we start seeing a whole bunch of chemical weapons moving around or being utilized," he told reporters. "That would change my calculus; that would change my equation."
4. Peace between Israel and Palestinians
Expectations are zero that Obama will broker peace between Netanyahu and Palestinian leader Mahmoud Abbas, who have yet to return to the negotiating table.
Still, Obama will visit Ramallah in the West Bank and meet with Abbas and Palestinian Authority Prime Minister Salam Fayyad -- if only to highlight the distance that remains for a two-state solution for Israel and the Palestinians.
5. Beyond the visit
After Obama visits Israel, the West Bank and then Jordan, new Secretary of State John Kerry will likely remain behind in Israel and meet with Netanyahu on Saturday, a senior State Department official told CNN.
Kerry would review the results of Obama's visit and discuss the next steps on key issues, the senior official said.
Such a follow-up strategy would mark Kerry's first foray into Mideast peace issues -- and could advance any success Obama achieves during his maiden visit to Jerusalem and the West Bank.