
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
Honza has a box of colored pencils in his pantry, which contains 5 blue, 9 red, 6 green, and 4 yellow pencils. It is dark, there is no light in the pantry, and Honza has no source of illumination. Therefore, he cannot distinguish the colors of the pencils.

a) What is the minimum number of pencils he must take to ensure that he has at least one pencil of each color?

b) What is the maximum number of pencils he can take to ensure that there is at least one pencil of each color remaining in the box?

c) What is the maximum number of pencils he can take to ensure that there are at least five red pencils remaining in the box?

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