
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 the sequence $\{a\_n\}$ is a geometric sequence with first term $a\_1=4$ and common ratio $q≠1$, and the sequence $4a\_1$, $a\_5$, $-2a\_3$ forms an arithmetic sequence, determine the value of the common ratio $q$

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