
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
For any real numbers \( x \) and \( y \), the operation is defined as
\[ x \oplus y = x + 2y + 3. \]

Given that real numbers \( a \) and \( b \) satisfy
\[ \left(a^3 \oplus a^2\right) \oplus a = a^3 \oplus \left(a^2 \oplus a\right) = b, \]

find the value of \( a + b \).

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