
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
We brought a cat named Vilda to our intended cottage to catch mice. On Monday, he caught $\frac{1}{2}$ of all the mice, on Tuesday $\frac{1}{3}$ of the remaining mice, on Wednesday $\frac{1}{4}$ of those left after Tuesday's catch, and on Thursday $\frac{1}{5}$ of the rest. On Friday, the remaining mice decided to move away. How many mice were originally at the cottage, given that on Friday, two more mice moved away than Vilda caught on Tuesday? Ensure that each day the number of mice caught was an integer.

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