
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 diagonals of convex quadrilateral  $BSCT$  meet at the midpoint  $M$  of  $\overline{ST}$ .  Lines  $BT$  and  $SC$  meet at  $A$ , and  $AB = 91$ ,  $BC = 98$ ,  $CA = 105$ .  Given that  $\overline{AM} \perp \overline{BC}$ , find the positive difference between the areas of  $\triangle SMC$  and  $\triangle BMT$ .

*Proposed by Evan Chen*

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