
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
There are $27$ unit cubes, and we are marking points on their faces. We are constructing a $3 \times 3 \times 3$ cube with these $27$ cubes. Calculate the least number of marked points on the faces of the new cube.

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