
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 number $m$ is randomly selected from the set $\{21, 23, 25, 27, 29\}$, and a number $n$ is randomly selected from $\{2010, 2011, 2012, \ldots, 2030\}$. Calculate the probability that $m^n$ ends in the digit $1$.

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