
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 the real number $\pi$ such that $\dfrac{31}{10} < \pi < \dfrac{49}{15}$, and after one application of the "Tuning Day Method" yields $\dfrac{16}{5}$ as a more accurate excessive approximation, determine the approximate fraction of $\pi$ after a fourth application of the "Tuning Day Method".

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