
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
Convert to polar coordinates and then evaluate the double integral \(I = \iint_{D} \frac{dx \, dy}{x^{2} + y^{2}}\), where \(D\) is the circular ring bounded by the circles \(x^{2} + y^{2} = 1\) and \(x^{2} + y^{2} = 4\) (i.e., \(1 \leq x^{2} + y^{2} \leq 4\)).

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