
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
The sides of rectangle  $ABCD$  have lengths 10 and 11.  An equilateral triangle is drawn so that no point of the triangle lies outside  $ABCD.$   The maximum possible area of such a triangle can be written in the form  $p\sqrt{q}-r,$  where  $p, q,$  and  $r$  are positive integers, and  $q$  is not divisible by the square of any prime number.  Find  $p+q+r.$ 

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