
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
A great person tells us: make progress every day, persevere, and the harvest will be more than just a little. If we consider the current learning situation of a student as $1$, with a daily "progress rate" of $3\%$, then after a semester (considered as $120$ days), the learning situation will be $\left(1+3\%\right)^{120}\approx 34.711$. If the daily "regress rate" is $3\%$, then after a semester, the learning situation will be $\left(1-3\%\right)^{120}\approx 0.026$. After a semester, the learning situation of the one who progresses is more than $1335$ times that of the one who regresses. In the above situation, if the value of "progress" is $1000$ times the value of "regress", the number of days needed to pass is approximately ______ days. (Round to the nearest whole number) (Reference data: $\lg 103\approx 2.013, \lg 97\approx 1.987$)

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