
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 bank plans to invest 40% of a certain fund in project M for one year, and the remaining 60% in project N. It is estimated that project M can achieve an annual profit of 19% to 24%, while project N can achieve an annual profit of 29% to 34%. By the end of the year, the bank must recover the funds and pay a certain rebate rate to depositors. To ensure that the bank's annual profit is no less than 10% and no more than 15% of the total investment in M and N, what is the minimum rebate rate that should be given to the depositors?

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