
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
On a plane, there are a finite number of polygons. If any two of these polygons have a line passing through the origin that intersects both of them, then these polygons are said to be properly placed. Find the smallest natural number \( m \) such that for any set of properly placed polygons, we can draw \( m \) lines passing through the origin such that each of these polygons intersects with at least one of these \( m \) lines.

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