
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]

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[ACTION NAME]

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# Your action step 2

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...

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Since the beginning of autumn this year, a certain city has experienced many days of haze weather, with severe air pollution. The city's environmental protection research institute conducted a survey and study on the daily air pollution situation recently and found that the relationship between the air pollution index and the time $x$ (hours) of the day is described by the function $f(x) = | \log_{25}(x+1) - a | + 2a + 1$, where $x \in [0, 24]$, and $a$ is the air management adjustment parameter, with $a \in (0, 1)$.
(1) If $a = \frac{1}{2}$, find the time of day when the city's air pollution index is the lowest;
(2) If the maximum value of $f(x)$ each day is considered as the daily air pollution index, to ensure that the city's daily air pollution index does not exceed 3, within what range should the adjustment parameter $a$ be controlled?

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