
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 $\{a\_n\}$, where $a\_2 = 6$ and $a\_3 + a\_6 = 27$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Let $S\_n$ denote the sum of the first $n$ terms in the sequence $\{a\_n\}$, and define $T\_n = \frac{S\_n}{3 \cdot 2^{n-1}}$. If $T\_n \leq m$ holds true for all positive integers $n$, find the range of possible values for the real number $m$.

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