
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
In the sequence $\{a_n\}$, $a_n = 32$, $s_n = 63$,

(1) If the sequence $\{a_n\}$ is an arithmetic sequence with a common difference of 11, find $a_1$;  
(2) If the sequence $\{a_n\}$ is a geometric sequence with the first term $a_1 = 1$, find the sum of the first $m$ terms of the sequence $\{a_m^2\}$, denoted as $s_m'$.

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