
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
To prepare for the peak summer tourist season, Shaolin Temple set up an exclusive inn for accommodating tourists. The temple staff noticed that some of the food prepared for tourists was left over in certain months, leading to significant waste. To control operational costs and minimize waste, they decided to adjust the supply accordingly. They tracked the number of tourists staying each month and discovered that the number of tourists staying at the inn each month showed periodic changes with the following patterns:
1. The same month each year, the number of tourists staying at the inn is basically the same;
2. The number of tourists staying is the least in February and the most in August, with a difference of about 400 people;
3. About 100 tourists stay in the inn in February, and the number increases each month until it reaches the maximum in August.
(a) Try to describe the relationship between the number of tourists staying in the inn and the month of the year with a sinusoidal trigonometric function;
(b) In which months should food for more than 400 people be prepared?

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