
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
Consider an arithmetic sequence $\\{a\_n\\}$ where $a\_n > 0$, $a\_2 + a\_5 + a\_8 = 33$, and $a\_1 + 2$, $a\_2 + 5$, $a\_3 + 13$ form the first three terms of a geometric sequence $\\{b\_n\\}$.

1. Find the general term formulas for the sequences $\\{a\_n\\}$ and $\\{b\_n\\}$.
2. Let $c\_n = \frac{a\_n}{b\_n} + 1$. Find the sum of the first $n$ terms of the sequence $\\{c\_n\\}$, denoted as $T\_n$.

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