
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
Yumi has a flat circular chocolate chip cookie with a radius of 3 cm. On the top of the cookie, there are \( k \) circular chocolate chips, each with a radius of 0.3 cm. No two chocolate chips overlap, and no chocolate chip hangs over the edge of the cookie. For what value of \( k \) is exactly \( \frac{1}{4} \) of the area of the top of the cookie covered with chocolate chips?

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