
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
If $0 \leq p \leq 1$ and $0 \leq q \leq 1$, define $F(p, q)$ by
\[
F(p, q) = -4pq + 5p(1-q) + 2(1-p)q - 6(1-p)(1-q).
\]
Define $G(p)$ to be the maximum of $F(p, q)$ over all $q$ in the interval $0 \leq q \leq 1$. What is the value of $p$ (in the interval $0 \leq p \leq 1$) that minimizes $G(p)$?

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