
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 the sequence $\{a_n\}$, it is known that when $p + q = 11$, $p, q \in \mathbb{N}^*, p < q$, $a_p + a_q = 2^p$, determine the sum of the first 10 terms of the sequence, denoted as $S_{10}$.

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