
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 points $F_1(-\sqrt{2}, 0)$ and $F_2(\sqrt{2}, 0)$, a moving point $P$ satisfies $|PF_2| - |PF_1| = 2$. When the ordinate of point $P$ is $\frac{1}{2}$, the distance from point $P$ to the origin is __________.

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