
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
On Černíček's farm, there were three hens. The first laid one egg every day, the second laid one egg every other day, and the third laid one egg every third day. Mr. Černíček bought two new hens from the market, which also laid eggs regularly - always one after a certain number of days, with one of them laying twice as often as the other.

Mrs. Černíčková calculated that in 60 days, all five hens laid a total of 155 eggs. How often did the new hens lay eggs?

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