
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Let triangle \(ABC\) have \(AB=5\), \(BC=6\), and \(AC=7\), with circumcenter \(O\). Extend ray \(AB\) to point \(D\) such that \(BD=5\), and extend ray \(BC\) to point \(E\) such that \(OD=OE\). Find \(CE\).

Present the answer in LaTex format: \boxed{Your answer}
user