
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) In how many different ways can we paint the circles in the letter "O," not necessarily using all 3 colors?

b) In how many different ways can we paint the circles in the letter "E," necessarily using all 3 colors?

c) In how many different ways can we paint the letter "B" such that circles connected by a segment must have different colors? (The three circles aligned vertically have TWO segments separating them).

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