
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 finite sequence $\{a\_1\}, \{a\_2\}, \ldots \{a\_m\} (m \in \mathbb{Z}^+)$ that satisfies the conditions: $\{a\_1\} = \{a\_m\}, \{a\_2\} = \{a\_{m-1}\}, \ldots \{a\_m\} = \{a\_1\}$, it is called a "symmetric sequence" with the additional property that in a $21$-term "symmetric sequence" $\{c\_n\}$, the terms $\{c\_{11}\}, \{c\_{12}\}, \ldots, \{c\_{21}\}$ form an arithmetic sequence with first term $1$ and common difference $2$. Find the value of $\{c\_2\}$.

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