
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
We flip a fair coin $n$ times. Let's assume that heads appear $m$ times. The number $\frac{m}{n}$ is called the frequency of heads. The number $m / n-0.5$ is called the deviation of the frequency from the probability, and the number $|m / n-0.5|$ is called the absolute deviation. Note that both deviation and absolute deviation are random variables. For instance, if the coin is flipped 5 times, and heads appear twice, then the deviation is $\frac{2}{5} - 0.5 = -0.1$, and the absolute deviation is 0.1.

The experiment consists of two parts: first, the coin is flipped 10 times, and then it is flipped 100 times. In which case is the mathematical expectation of the absolute deviation of the frequency of heads from the probability greater?

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