
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
In triangle  $ABC$ , angles  $A$  and  $B$  measure 60 degrees and 45 degrees, respectively.  The bisector of angle  $A$  intersects  $\overline{BC}$  at  $T$ , and  $AT=24.$   The area of triangle  $ABC$  can be written in the form  $a+b\sqrt{c},$  where  $a$ ,  $b$ , and  $c$  are positive integers, and  $c$  is not divisible by the square of any prime.  Find  $a+b+c.$ 

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