
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
A rhombus  $ABCD$  is given with  $\angle BAD = 60^o$  . Point  $P$  lies inside the rhombus such that  $BP = 1$ ,  $DP = 2$ ,  $CP = 3$ . Determine the length of the segment  $AP$ .

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