
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 $\{a_n\}$ satisfying $a_1 = -1$, $a_2 > a_1$, and $|a_{n+1} - a_n| = 2^n$ (where $n \in \mathbb{N}^*$). If the subsequence $\{a_{2n-1}\}$ is monotonically decreasing, and the subsequence $\{a_{2n}\}$ is monotonically increasing, then the general term formula for the sequence $\{a_n\}$ is $a_n =$ ________.

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