
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
Where is the deviation greater? We toss a fair coin $n$ times. Suppose heads comes up $m$ times. The number $m/n$ is called the frequency of heads. The number $\frac{m}{n} - 0.5$ is called the deviation of the frequency from probability, and the number $\left|\frac{m}{n} - 0.5\right|$ is called the absolute deviation. Note that the deviation and absolute deviation are random variables. For example, if the coin is tossed 5 times and heads comes up twice, then the deviation is $\frac{2}{5} - 0.5 = -0.1$, and the absolute deviation is $|-0.1| = 0.1$.

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

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