
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
A permutation of $1, 2, \cdots, n$ (where $n \geq 2$) is called a "good permutation" if there exists exactly one $i \in \{2, 3, \cdots, n\}$ such that $a_i < a_{i-1}$. If the number of good permutations is $p_n$, then evaluate $\sum_{i=2}^{n} \frac{p_i}{2^i}$.

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