
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
A shape obtained by removing one unit square from a $2 \times 2$ square grid is called an "L-shape." In an $8 \times 8$ square grid, $k$ L-shapes are placed where each L-shape can be rotated but must exactly cover three unit squares, and any two L-shapes must not overlap. Additionally, no other L-shapes can be placed on the grid except for these $k$ L-shapes. Find the minimum value of $k$.

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