
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
Let P be a point on the curve $2x = \sqrt{4 + y^2}$, A($-\sqrt{5}$, 0), B($\sqrt{5}$, 0). If $|PB| = 2$, then $|PA| = \_\_\_\_\_\_.$

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