
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 that a student's normal heart rate is $80$, the physical health coefficient $k=7$, and the heart rate $y$ (unit: beats per minute) after push-ups satisfies $y=80(\ln\sqrt{\frac{x}{12}}+1)$, where $x$ is the number of push-ups, determine the most appropriate number of sets of push-ups, with each set consisting of $12$ repetitions, required to achieve a moderate intensity exercise, defined as $28 < f(t) < 34$, where $f(t) = ke^{t}$ and $t = \frac{y}{80}$.

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