
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
Given $f(x) = 2x^3 + ax$ and $g(x) = bx^2 + c$, both graphs pass through point $P(2, 0)$, and they have a common tangent line at point $P$. Find the expressions for $f(x)$ and $g(x)$.

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