
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  $\triangle ABC$  with  $AB=AC$  and  $BC=14$  be inscribed in a circle  $\omega$ . Let  $D$  be the point on ray  $BC$  such that  $CD=6$ . Let the intersection of  $AD$  and  $\omega$  be  $E$ . Given that  $AE=7$ , find  $AC^2$ .

*Proposed by Ephram Chun and Euhan Kim*

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