
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 \\(F(1,0)\\), point \\(M\\) be on the \\(x\\)-axis, and point \\(P\\) be on the \\(y\\)-axis, with \\(\overrightarrow{MN}=2\overrightarrow{MP}\\) and \\(\overrightarrow{PM} \perp \overrightarrow{PF}\\). When point \\(P\\) moves along the \\(y\\)-axis, the equation of the trajectory of point \\(N\\) is \_\_\_\_\_\_\_\_.

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