
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
Each face of a cube is painted with exactly one colour. Given that no two faces that share an edge are the same colour, determine the smallest number of colours needed to paint the cube.

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