
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
Jeff has a deck of  $12$  cards:  $4$   $L$ s,  $4$   $M$ s, and  $4$   $T$ s. Armaan randomly draws three cards without replacement. The probability that he takes  $3$   $L$ s can be written as  $\frac{m}{n}$ , where  $m$  and  $n$  are relatively prime positive integers. Find  $m +n$ .

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