
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 cell in a $3 \times 4$ grid is either free or contains a hidden mine. In two cells free of mines, the number of mines located in neighboring cells is indicated (see the diagram).

How many ways can the mines be placed in the closed cells? Cells that share a side or a vertex are considered neighboring.

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