
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
The relationship between the average monthly temperature and the month in a certain city throughout the year can be approximately represented by the trigonometric function $$y=a+A\cos\left[\frac{\pi}{6}(x-6)\right]$$ where $x=1, 2, 3, \ldots, 12$. It is known that the average monthly temperature reaches its maximum in June, at 28°C, and its minimum in December, at 18°C. Find the average temperature in October.

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