
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

Let the geometric sequence $\left\{a_{n}\right\}$ have the first term $a_{1}=a$ and common ratio $q \neq 1$. Find the sum of all distinct products of any two different terms for the first $n$ terms of this sequence.

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