
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
Compute the double integral \( I = \int_{D} \int (x+y) \, dx \, dy \), where \( D \) is the region bounded by the lines \( x=0 \), \( y=x^{2}+x-3 \), and \( 2y=3x \) (for \( x \geq 0 \)).

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