
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 parabola has the following optical properties: a light ray passing through the focus of the parabola and reflecting off the parabola will result in a light ray parallel to the axis of symmetry of the parabola; conversely, an incident light ray parallel to the axis of symmetry of the parabola will, after reflecting off the parabola, pass through the focus of the parabola. Given that the focus of the parabola $y^{2}=4x$ is $F$, a light ray parallel to the x-axis is emitted from point $A(5,4)$, reflects off point $B$ on the parabola, and then exits through another point $C$ on the parabola. Find the value of $|BC|$.

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