
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
Some cells (unit cubes) in a 2015-edged cube grid are infected by an unknown infection. The infection spreads such that if at least \( t \) cells in a row parallel to one of the cube's edges are infected (\(1 \leq t \leq 2015\)), then one minute later, all cells in that row become infected. Determine the number of initially infected cells for which

a) it becomes possible,

b) we can be certain,

that the infection will spread to all cells in the cube.

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