
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
For each positive integer  $n$ , consider the highest common factor  $h_n$  of the two numbers  $n!+1$  and  $(n+1)!$ . For  $n<100$ , find the largest value of  $h_n$ .

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