
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 the sequence $\{a\_n\}$, where $a\_n=32$, and the sum of the first $n$ terms is $S\_n=63$.

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, $T\_m$, of the sequence $\{a \;\_{ n }^{ 2 }\}$.

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