
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
Let the function $f(x) = x^3 + 2ax^2 + bx + a$, $g(x) = x^2 - 3x + 2$, where $x \in \mathbb{R}$, and $a$, $b$ are constants. It is known that the curve $y = f(x)$ and $y = g(x)$ have the same tangent line $l$ at the point $(2, 0)$ on their graphs. Find the values of $a$ and $b$, and write the equation of the tangent line $l$.

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