
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 a geometric sequence $\{a_n\}$ with a common ratio $q$ has a sum of its first 6 terms, $S_6 = 21$, and $2a_1$, $\frac{3}{2}a_2$, $a_3$ form an arithmetic sequence.

(1) Find the general term formula for the sequence $\{a_n\}$.
(2) Let $\{b_n\}$ be an arithmetic sequence with the first term 2 and common difference $-a_1$, and its sum of the first $n$ terms as $T_n$. Find the solution set for the inequality $T_n - b_n > 0$.

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