
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 an arithmetic sequence $\{a\_n\}$ with a common ratio $q \neq 1$ that satisfies the following conditions: $a\_1 + a\_2 + a\_3 + a\_4 + a\_5 = 6$, $a\_1^2 + a\_2^2 + a\_3^2 + a\_4^2 + a\_5^2 = 18$, find the value of $a\_1 - a\_2 + a\_3 - a\_4 + a\_5$.

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