
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]

# Your action step 1

# Your action step 2

# Your action step 3

...

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The temperature of a laboratory on a given day, represented in degrees Celsius, changes approximately with time $t$ (in hours) according to the function: $f(t)=10-\sqrt{3}\cos{\frac{\pi}{12}t}-\sin{\frac{\pi}{12}t},t\in[0,24)$.

(1) Determine the maximum temperature difference in the laboratory for the day.

(2) If it is required that the laboratory temperature does not exceed $11^{\circ} \text{C}$, during which time period should the laboratory's temperature be lowered?

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