
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 \( p \) be a given positive even number. The sum of all elements in the set \( A_{p}=\left\{x \mid 2^{p}<x<2^{p+1}, x=3m, m \in \mathbf{N}\} \) is \(\quad\).

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