
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
Let  $M$  be on segment $ BC$  of  $\vartriangle ABC$  so that  $AM = 3$ ,  $BM = 4$ , and  $CM = 5$ . Find the largest possible area of  $\vartriangle ABC$ .

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