
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
Given the average score of the morning session is 90, and the average score of the afternoon session is 75, and the ratio of the number of students in the morning session to the afternoon session is $\frac{4}{5}$, calculate the mean score of all the students combined.

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