
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
Assuming that the scores of the second mock exam in Nanchong City each year generally reflect the performance of the city's candidates in the college entrance examination for that year. Suppose in a certain year, the science scores of the second mock exam follow a normal distribution $\xi \sim N(480, 100^2)$. If the admission rate to first-tier universities in previous years was 40%, then the possible cut-off score for admission to first-tier universities is (given that $\Phi(0.25) = 0.6$).

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