
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
Vasya solved problems for 15 days - at least one problem each day. Each day (except the first), if the weather was cloudy, he solved one more problem than the previous day, and if it was sunny, he solved one problem less. Over the first 9 days, Vasya solved 13 problems.

a) What was the weather like on the 10th day? How many problems did he solve on that day?

b) What is the maximum number of problems Vasya could have solved on the 15th day?

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