
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
Find the remainder of the polynomial \(P(x)=x^{6 n}+x^{5 n}+x^{4 n}+x^{3 n}+x^{2 n}+x^{n}+1\) when divided by \(Q(x)=x^{6}+x^{5}+x^{4}+x^{3}+x^{2}+x+1\), given that \(n\) is a multiple of 7.

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