
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 geometric sequence $\{a_n\}$ with a common ratio $q \neq 1$ and satisfying: $a_1+a_2+a_3+\ldots+a_7=6$, $a_1^2+a_2^2+a_3^2+\ldots+a_7^2=18$, find the value of $a_1-a_2+a_3-a_4+a_5-a_6+a_7$.

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