
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 an arithmetic sequence $\{a\_n\}$ with a common difference greater than $0$, $2a\_7 - a_{13} = 1$, and $a\_1$, $a\_3 - 1$, $a\_6 + 5$ form a geometric sequence. Find the sum of the first 21 terms of the sequence $\{(-1)^{n-1}a\_n\}$.

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