
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
Observe the following equations: $(x^2+x+1)^0=1$; $(x^2+x+1)^1=x^2+x+1$; $(x^2+x+1)^2=x^4+2x^3+3x^2+2x+1$; $(x^2+x+1)^3=x^6+3x^5+6x^4+7x^3+6x^2+3x+1$; ...; It can be inferred that in the expansion of $(x^2+x+1)^5$, the sum of the coefficients of the fifth, sixth, and seventh terms is $\boxed{141}$.

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