
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
For the parabola $C$, suppose a line $l$ passes through the focus $F$ of $C$, and the angle between $l$ and the axis of symmetry of $C$ is $\frac{\pi}{4}$. If the chord intercepted by $l$ on $C$ has a length of 4, then the distance from the focus of $C$ to its vertex is ______.

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