
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
The Dingoberry Farm is a 10 mile by 10 mile square, divided into 1 mile by 1 mile patches. Each patch is farmed by either Farmer Keith or Farmer Ann. If Ann farms a patch, she also farms all patches directly west and south of it. Ann places a scarecrow on each of her patches that is adjacent to exactly two of Keith's patches. If Ann farms a total of 30 patches, what is the largest number of scarecrows she could place?

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