
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
For the function \( y = (n-1) t^2 - 10t + 10, \; t \in (0,4] \), does there exist a positive integer \( n \) such that \( 0 < y \leq 30 \) always holds?

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