
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
Consider the family of lines $M$:
\[x \cos \theta + (y - 2) \sin \theta = 1 \quad (0 \leqslant \theta \leqslant 2 \pi).\]
For the following four statements:
1. All lines in the family $M$ pass through a fixed point.
2. There exists a fixed point $P$ not on any line in the family $M$.
3. For any integer \( n \) (\( n \geqslant 3 \)), there exists a regular $n$-sided polygon with all its sides lying on lines in the family $M$.
4. The area of triangles formed by any three distinct lines in the family $M$ is always equal.

Identify the true statements. (Write down the numbers of all true statements).

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