
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 $\{a_n\}$, where $a_2 + a_3 = 14$ and $a_4 - a_1 = 6$.

(1) Find the general formula for the sequence $\{a_n\}$.
(2) Let $\{b_n\}$ be a geometric sequence satisfying $b_2 = a_1$ and $b_3 = a_3$. If $b_6 = a_m$, find the value of the real number $m$.

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