
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 $\{a\_n\}$, let $S\_n$ be the sum of its first $n$ terms. If $S\_9 > 0$ and $S\_{10} < 0$, find the largest term in the sequence $\{\frac{2}{a\_1}, \frac{2^2}{a\_2}, ..., \frac{2^9}{a\_9}\}$.

A) $\frac{2}{a\_1}$
B) $\frac{2^5}{a\_5}$
C) $\frac{2^6}{a\_6}$
D) $\frac{2^9}{a\_9}$

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