
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 $x$'s insufficient approximation and excessive approximation as $\frac{b}{a}$ and $\frac{d}{c}$ respectively ($a, b, c, d \in \mathbb{N}^*$), then $\frac{b+d}{a+c}$ is a more accurate insufficient or excessive approximation of $x$. We know $\pi = 3.14159\ldots$, if we let $\frac{31}{10} < \pi < \frac{49}{15}$, then after the first application of the "Tuning Day Method", we get $\frac{16}{5}$ as a more accurate excessive approximation of $\pi$, i.e., $\frac{31}{10} < \pi < \frac{16}{5}$. Determine the approximate fraction of $\pi$ after the fourth application of the "Tuning Day Method".

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