
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 \( y = 5 \sin \left( \frac{2m+1}{3} \pi x + \frac{\pi}{3} \right) \) (where \( m \in \mathbf{N} \)), for any real number \( a \), in the interval \([a, a+3]\), the value of \( y \) is equal to \( \frac{5}{4} \) no less than 4 times and no more than 8 times. Find the value of \( m \).

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