
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

Dima has an unusual dice. Its faces are also numbered from 1 to 6, but the faces with even numbers appear with twice the probability of the faces with odd numbers (faces with the same parity appear with equal probability). Dima found the probability that the number of points rolled does not exceed three, wrote it as an irreducible fraction \( \frac{m}{n} \), and found the sum \( m+n \). What number did Dima get?

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