
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 bear is in the center of the left down corner of a  $100*100$  square .we call a cycle in this grid a bear cycle if it visits each square exactly ones and gets back to the place it started.Removing a row or column with compose the bear cycle into number of pathes.Find the minimum  $k$  so that in any bear cycle we can remove a row or column so that the maximum length of the remaining pathes is at most  $k$ .

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