
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
Consider the polynomial \( Q(x) = x^3 + px^2 + qx + d \) where the mean of its zeros, the product of its zeros taken two at a time, and the sum of its coefficients are all equal. If the \( y \)-intercept of the graph of \( y = Q(x) \) is 7, determine the value of \( q \).

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