
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
Contractor Alice agreed to complete a painting job in 40 days. After 10 days, she found that the 12 people assigned to the work had already completed $\frac{1}{4}$ of the job. However, due to a scheduled increase in efficiency (by doubling the work rate), the team's productivity will increase starting from day 20. If everyone works at the same rate, what is the least number of people Alice must keep on the job to ensure that the job is completed on time?

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