
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
We have 50 numbered chips from 1 to 50, and they need to be colored either red or blue. We know that chip 5 is blue. For the coloring of the remaining chips, the following rules are followed:

a) If the chip with number $x$ and the chip with number $y$ are of different colors, then the chip with number $|x-y|$ is painted red.

b) If the chip with number $x$ and the chip with number $y$ are of different colors and $x \cdot y$ is a number between 1 and 50 (inclusive), then the chip with number $x \cdot y$ is painted blue.

Determine how many different colorings can be made on the set of chips.

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