
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
In a 7x7 square grid, 4 unit squares are initially shaded at positions $(3,7)$, $(6,3)$, $(1,4)$, and $(7,1)$. Determine the minimum number of additional unit squares that must be shaded to ensure the grid has both horizontal and vertical lines of symmetry.

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