
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
Equilateral triangle \(ABC\) has a side length of \(\sqrt{144}\). Another triangle \(AD_1E_1\) is congruent to triangle \(ABC\), with \(D_1\) located such that \(BD_1 = \sqrt{16}\). Find the square of the length \(CE_1\).

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