
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
An embankment construction project initially planned for $100$ workers to complete in $5$ days. However, after starting the project, it was found that $40$ workers had to be reassigned after $2$ days to a more urgent task. The remaining workers completed the original task, but at a rate of $\frac{3}{4}$ of their original productivity. How many additional days were needed to complete the embankment?

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