
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 die. Its faces also have numbers from 1 to 6, but the faces with an even number of spots occur with twice the probability of faces with an odd number of spots (faces with numbers of the same parity occur with the same probability). Dima found the probability that the number of points rolled does not exceed three, recorded it as an irreducible fraction \( m / n \), and then found the sum \( m+n \). What number did Dima get?

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