
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 courier leaves point $A$ and travels 10 leagues the first day, and on each subsequent day, he travels $\frac{1}{4}$ league more than the previous day. Three days later, another courier leaves point $B$, which is 40 leagues from point $A$, and travels in the same direction. On the first day, he travels seven leagues, and on each subsequent day, he increases his distance by $\frac{2}{3}$ league more than the previous day. How many days after the first courier's departure will the two couriers meet?

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