
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 an arithmetic sequence $\{a\_n\}$ that satisfies $a\_3 + a\_6 = -\frac{1}{3}$, $a\_1a\_8 = -\frac{4}{3}$, and $a\_1 > a\_8$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Create a new sequence $\{b\_n\}$ using the first, fourth, seventh, ..., $(3n - 2)$-th, ... terms of $\{a\_n\}$ as its first, second, third, ..., $n$-th, ... terms. Find the sum of all terms in the sequence $\{2^{b\_n}\}$.

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