
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 $P_{1}(2,-1)$, $P_{2}(0,5)$, and point $P$ is on the extension line of $P_{1}P_{2}$, with $| \overrightarrow{P_{1}P}|=2| \overrightarrow{PP_{2}}|$, find the coordinates of point $P$.

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