
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 school admits art-talented students based on their entrance exam scores. It enrolls $\frac{2}{5}$ of the candidates, whose average score is 15 points higher than the admission cutoff score. The average score of the candidates who were not admitted is 20 points lower than the cutoff score. If the average score of all candidates is 90 points, determine the admission cutoff score.

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