
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 right triangle \( \triangle ABC \) with \( \angle C = 90^{\circ} \) and \( AB = 1 \), point \( E \) is the midpoint of side \( AB \), and \( CD \) is the altitude from \( C \) to \( AB \). Find the maximum value of \( (\overrightarrow{CA} \cdot \overrightarrow{CD}) \cdot (\overrightarrow{CA} \cdot \overrightarrow{CE}) \).

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