
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
On the parabola $y^{2}=6x$, a point $P(x_{0},y_{0})$ intersects the parabola with two lines at points $A$ and $B$. If the slope of line $AB$ is $2$, and the sum of the reciprocals of the slopes of lines $PA$ and $PB$ is $3$, calculate the value of $y_{0}$.

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