
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
Alyosha has 100 closed boxes in front of him, each containing either a red or a blue cube. Alyosha has one ruble in his account.

a) There is only one blue cube.

b) There are exactly $n$ blue cubes.

(Alyosha can also choose to bet 0, meaning he can open a box for free and see the color of the cube.)

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