
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
Inside a parallelogram \(A B C D\), an arbitrary point \(P\) is chosen, and segments \(P A, P B, P C,\) and \(P D\) are drawn. The areas of three of the resulting triangles are 1, 2, and 3 (in some order). What values can the area of the fourth triangle take?

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