
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 that $f(x)$ is an odd function defined on $\mathbb{R}$, and when $x \ge 0$, $f(x) = 2x^2$.
1. Find the expression for $f(x)$ when $x < 0$;
2. Let $g(x) = \ln x$. Determine if there exists some $x_0$ such that the tangent lines to $f(x)$ and $g(x)$ at $x = x_0$ are parallel. If such an $x_0$ exists, find its value. If it does not exist, explain why.

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