
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
Given triangle $\triangle ABC$, where $\angle BAC = \angle BCA$, $AB = 5$ cm, $BC = 6$ cm, and $CA = 6$ cm, extend $AB$ to $D$ such that $BD = 2.5$ cm, determine the length of $CD$.

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