
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
Among the following four propositions: 
1. If $x^2 = 2003 \times 2005 + 1$, then $x = 2004$;
2. A quadrilateral with equal and perpendicular diagonals must be either a square or an isosceles trapezoid;
3. Using the same length of material to enclose an area on the ground into either a square or a circle, the area of the circle will be larger;
4. Three non-coincident planes in space can divide the space into 4, 6, 7, or 8 parts. The correct proposition numbers are.

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