
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
A person throws two fair dice at the same time (their six faces are marked with the numbers 1, 2, 3, 4, 5, 6 respectively).

Find: (1) The probability that the two dice show the same number;

   (2) The probability that the sum of the numbers on the two dice is a multiple of 5.

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