
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 a sequence $\{a_n\}$ where $a_1 = -1$, $a_2 > a_1$, and $|a_{n+1}-a_n| = 2^{n}$ for $n \in \mathbb{N}^*$, if the subsequence $\{a_{2n-1}\}$ is monotonically decreasing and the subsequence $\{a_{2n}\}$ is monotonically increasing, then find the general term of the sequence $\{a_n\}$: $a_n = \_\_\_$.

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