
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 that the sequence $\{a_n\}$ is an arithmetic progression with a common difference of 2, and $a_3 + 1$ is the geometric mean of $a_1 + 1$ and $a_7 + 1$.

1. Find the general term formula for the sequence $\{a_n\}$.
2. Find the sum $T_n$ of the first $n$ terms of the sequence $\{\frac{1}{a_n \cdot a_{n+1}}\}$.

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