
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 the parabola $C:y^{2}=2px\left(p \gt 0\right)$ with focus $F$, and $K$ as the intersection point of the directrix $l$ of $C$ and the x-axis. A line passing through point $K$ with a slope of $45^{\circ}$ intersects the parabola $C$ at only one point $P\left(3,t\right)$. Find the value of $t$.

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