
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 recruits students with special talents in art based on their entrance exam scores and determines a cut-off score for admission. The school admits $\frac{2}{5}$ of the candidates. The average score of all admitted candidates is 15 points higher than the cut-off score, while the average score of the candidates who were not admitted is 20 points lower than the cut-off score. If the average score of all candidates is 90 points, what is the cut-off score for admission?

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