
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
A student observed the weather continuously for $n$ days and the observations were as follows:
① There were 5 afternoons with clear skies;
② There were 7 mornings with clear skies;
③ There were 8 half-days with rain;
④ On the days it rained in the afternoon, the mornings were clear.
Find the number of days $n$ that the student observed.

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