
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
In the Cartesian coordinate system $xOy$, given the parabola $(E): y^2 = 2px (p > 0)$ with focus $F$, $P$ is an arbitrary point on the parabola $(E)$ in the first quadrant, and $Q$ is a point on the line segment $PF$ such that $\overrightarrow{OQ} = \frac{2}{3} \overrightarrow{OP} + \frac{1}{3} \overrightarrow{OF}$. Determine the maximum slope of the line $OQ$.

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