
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 equilateral triangle ABC, point P is positioned such that the perpendicular distances from P to sides AB, BC, and CA are denoted by Q, R, and S respectively. If PQ = 2, PR = 3, and PS = 4, what is the length of AB expressed in radicals?

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