
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 that the sequence $\{|a\_n|\}$ is an arithmetic sequence with first term and common difference both equal to $1$, find $a\_2 =$ \_\_\_\_\_\_ . If $S\_2 = a\_1 + a\_2$, find the set of all possible values of $S\_2$ .

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