
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
(1) Given an arithmetic sequence $\{a_n\}$ with a common difference of $d$ ($d \neq 0$), and $a_3 + a_6 + a_{10} + a_{13} = 32$. If $a_m = 8$, then $m = \boxed{8}$.

(2) Let the sum of the first $n$ terms of an arithmetic sequence $\{a_n\}$ be $S_n$. If $S_3 = 9$ and $S_6 = 36$, then $a_7 + a_8 + a_9 = \boxed{45}$.

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