
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 4x5 rectangle grid, 3 of the unit squares have already been colored. These squares are located at positions (1,4), (2,1), and (4,2). What is the least number of additional unit squares that must be shaded so that the rectangle has two lines of symmetry—one horizontal and one vertical—and includes rotational symmetry?
- **A) 7**
- **B) 8**
- **C) 9**
- **D) 10**
- **E) 11**

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