
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 *strip* is the region between two parallel lines.  Let  $A$  and  $B$  be two strips in a plane.  The intersection of strips  $A$  and  $B$  is a parallelogram  $P$ .  Let  $A'$  be a rotation of  $A$  in the plane by  $60^\circ$ .  The intersection of strips  $A'$  and  $B$  is a parallelogram with the same area as  $P$ .  Let  $x^\circ$  be the measure (in degrees) of one interior angle of  $P$ .  What is the greatest possible value of the number  $x$ ?

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