
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
From a point $P$ on the directrix $l$ of the parabola $y^{2}=4x$, two tangents $PA$ and $PB$ are drawn to the parabola, with $A$ and $B$ being the points of tangency. If the slope angle of line $AB$ is $\frac{\pi}{3}$, determine the ordinate of point $P$.

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