
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
Given that $O$ is the origin, a perpendicular line $l$ is drawn through point $P(2,1)$ to line $OP$. Line $l$ intersects the parabola $y^{2}=2px$ ($p \gt 0$) at points $A$ and $B$, with $Q$ being the midpoint of segment $AB$. If triangle $OPQ$ is a right isosceles triangle, solve for the value of $p$.

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