
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 $\{a_n\}(n\in \mathbb{N}^*)$ is an arithmetic progression with a non-zero common difference, $a_1=1$, and $(a_2,a_4,a_8)$ forms a geometric progression.

(1) Find the general term formula for the sequence $\{a_n\}$.

(2) Let $b_n=\frac{1}{a_n a_{n+1}}$. Denote the sum of the first $n$ terms of the sequence $\{b_n\}$ as $T_n$. Find the maximum positive integer value of $n$ that satisfies $100T_n < 99$.

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