
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
A line is drawn from the origin $O$ to intersect the line $2x+4y-1=0$ at point $M$. Let $P$ be a point on line segment $OM$, given that $OP \cdot OM = 1$, find the polar equation of the curve on which point $P$ lies.

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