
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 finite set of polygons on a plane is considered properly placed if, for any two polygons in the set, there exists a line passing through the origin that intersects both. 

Find the smallest natural number \( m \) such that for any properly placed set of polygons, one can draw \( m \) lines passing through the origin such that each polygon in the set intersects at least one of these \( m \) lines.

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