
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 $\{a_n\}$ with the sum of its first $n$ terms denoted as $S_n$. It is known that $S_4 - S_2 = 7a_1$ and $S_5 = 30$.

(1) Find the general term formula $a_n$ for the sequence.
(2) Let $b_n = \frac{1}{S_n}$. The sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$, satisfies $T_n < \log_2(m^2 - m)$ for any $n \in \mathbb{N}^*$. Find the range of values for the real number $m$.

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