
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
The "Tiao Ri Method", invented by mathematician He Chengtian during the Southern and Northern Dynasties of China, is an algorithm for finding a more accurate fraction to represent a numerical value. Its theoretical basis is as follows: If the deficient approximate value and the excess approximate value of a real number $x$ are $\frac{b}{a}$ and $\frac{d}{c}$ ($a, b, c, d \in \mathbb{N}^*$) respectively, then $\frac{b+d}{a+c}$ is a more accurate deficient approximate value or excess approximate value of $x$. We know that $\pi = 3.14159...$, and if we let $\frac{31}{10} < \pi < \frac{49}{15}$, then after using the "Tiao Ri Method" once, we get $\frac{16}{5}$ as a more accurate excess approximate value of $\pi$, i.e., $\frac{31}{10} < \pi < \frac{16}{5}$. If we always choose the simplest fraction, then what approximate fraction can we get for $\pi$ after using the "Tiao Ri Method" four times?

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