
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
A line passing through the focus $F$ of the parabola $x^{2}=4y$ intersects the parabola at points $P_{1}(x_{1}, y_{1})$ and $P_{2}(x_{2}, y_{2})$. If $y_{1}+y_{2}=6$, calculate the value of $|P_{1}P_{2}|$.

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