
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
How many times must a die be rolled so that the probability of the inequality

\[ \left| \frac{m}{n} - \frac{1}{6} \right| \leq 0.01 \]

is at least as great as the probability of the opposite inequality, where \( m \) is the number of times a specific face appears in \( n \) rolls of the die?

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