
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 sequence $\{a_n\}$ defined for all positive integers $n$ such that $a_{n+2} = a_n a_{n+1} - c$ where $c$ is a constant, determine the condition for the sequence to be a geometric progression with respect to $a_1$, $a_2$, and $c$.

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