
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 a triangular pyramid \( S-ABC \) with a base that is an equilateral triangle with side length \( 4\sqrt{2} \) cm, and edge \( SC \) perpendicular to the base \( ABC \), and its length is 2 cm. Points \( D \) and \( E \) are the midpoints of \( AB \) and \( BC \) respectively. If point \( P \) moves along \( SE \), find the minimum value of the area of \( \triangle PCD \).

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