
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
Let the set \( A = \left\{ \frac{1}{2}, \frac{1}{7}, \frac{1}{11}, \frac{1}{13}, \frac{1}{15}, \frac{1}{32} \right\} \) have non-empty subsets \( A_1, A_2, \cdots, A_{63} \). Denote the product of all elements in the set \( A_i \) as \( p_i \) (the product of a single-element set is the element itself), \( i=1,2, \cdots, 63 \). Find \( p_1 + p_2 + \cdots + p_{63} \).

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