
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
 $ABC$  is an equilateral triangle and  $l$  is a line such that the distances from  $A, B,$  and  $C$  to  $l$  are  $39, 35,$  and  $13$ , respectively. Find the largest possible value of  $AB$ . 

*Team #6*

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