
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 point P(-2,0) and the parabola C: y^2=4x, let A and B be the intersection points of the line passing through P and the parabola. If |PA|= 1/2|AB|, find the distance from point A to the focus of parabola C.

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