
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
Bibliophile Vasya has 1300 books arranged on $k$ bookshelves. One day, Vasya rearranged the bookshelves to a new place, after first removing all the books. In the process, he completely forgot how the books were previously arranged, and placed them back on the shelves in a different order. What is the maximum $k$ for which there will definitely be 5 books that stood on the same shelf both before and after the rearrangement?

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