
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
Jesse has ten squares, which are labeled  $1, 2, \dots, 10$ . In how many ways can he color each square either red, green, yellow, or blue such that for all  $1 \le i < j \le 10$ , if  $i$  divides  $j$ , then the  $i$ -th and  $j$ -th squares have different colors?

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