
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
Consider a $4 \times 4$ grid. At each step, you choose a row, a column, or a main diagonal, and flip all the 0's in that line to 1's, and vice versa. For which of the following grids is it possible to transform the grid to one containing only 0's?

$$
\left(\begin{array}{llll}
0 & 1 & 1 & 0 \\
1 & 1 & 0 & 1 \\
0 & 0 & 1 & 1 \\
0 & 0 & 1 & 1
\end{array}\right)
$$

$$
\left(\begin{array}{llll}
0 & 1 & 0 & 0 \\
1 & 1 & 0 & 1 \\
0 & 0 & 0 & 1 \\
1 & 0 & 1 & 1
\end{array}\right)
$$

$$
\left(\begin{array}{llll}
0 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 \\
0 & 1 & 0 & 1 \\
1 & 0 & 0 & 1
\end{array}\right)
$$

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