
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
Nine cells of a $10 \times 10$ grid are infected. At each step, a cell becomes infected if it was already infected or if it had at least two infected neighboring cells (among the 4 adjacent cells).

(a) Can the infection spread to the entire grid?

(b) How many initially infected cells are required to spread the infection to the entire grid?

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