
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
In an opaque bag, there are $5$ red balls and $m$ yellow balls. All the balls are identical except for their colors. A student conducted the following experiment: randomly drawing $1$ ball from the bag, noting its color, putting it back, and shaking it evenly, which is considered as one trial. Based on the data of the ball-drawing experiments recorded in the table below, estimate the value of $m$ to be ____.

| Total number of trials $a$ | $100$ | $500$ | $1000$ | $2000$ | $\ldots $ |
|---------------------------|-------|-------|--------|--------|-----------|
| Number of times red ball is drawn $b$ | $19$ | $101$ | $199$ | $400$ | $\ldots $ |
| Frequency of drawing red ball $\frac{b}{a}$ | $0.190$ | $0.202$ | $0.199$ | $0.200$ | $\ldots $ |

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