
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 that the parabola $C: y^2 = x$ has a focus at point $F$, and $A(x_0, y_0)$ is a point on $C$ with $|AF| = \frac{5}{4}x_0$, find the value of $x_0$.

A) $2$
B) $1$
C) $4$
D) $8$

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