
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
In triangle  $ABC$  let  $D$  be the foot of the altitude from  $A$ . Suppose that  $AD = 4$ ,  $BD = 3$ ,  $CD = 2$ , and  $AB$  is extended past  $B$  to a point  $E$  such that  $BE = 5$ . Determine the value of  $CE^2$ .

*Ray Li.*

<details><summary>Clarifications</summary>[list=1][*]Triangle  $ABC$  is acute.[/list]</details>

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