
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 the garden, Anna and Vitya had 2006 rosebushes. Vitya watered half of all the bushes, and Anna watered half of all the bushes. It turned out that exactly three of the most beautiful bushes were watered by both Anna and Vitya. How many rosebushes remained unwatered?

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