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The Obama administration has all but ruled out sending US ground troops into front-line combat action in the Middle East.
At the same time, the US has struggled to build an effective force with partners on the ground to defeat both the Islamic State and the Syrian President Bashar al-Assad.
During their exchange at the Council on Foreign Relations, Clinton noted that Assad "has killed far more Syrians than ISIS has to date."
This prompted Zakaria to ask a rather pointed question about how difficult it would be to stabilize Syria:
If the only way you could put together a moderate Syrian force is by having the United States cajole, bribe, arm, and train it. We are then looking for this force to defeat ISIS, then defeat Assad, then defeat al-Nusra,then defeat other al Qaeda affiliates, keep at bay the Shiite militias and Hezbollah, taken control of Damascus, and establish a pluralistic democracy in Syria. Isn't that kind of a tall order?
"Certainly described like that!" Clinton replied to laughs.
The Democratic presidential front-runner said she planned to prioritize defeating the "common enemy of ISIS."
"And that's why I focused on ISIS. Because I think right now we have one overriding goal, as I outlined. We need to crush their territorial domain and we need to try and secure the entire border between Syria and Turkey," she said.
"There is not going to be a successful military effort at this point to overturn Assad," Clinton continued. "That can only happen through the political process. So our effort should be focused on ISIS."