
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 $x < 0$, $f(x) = \log_{2}(-x) - 2^{x}$.  
$(1)$ Find $f(0) - f(2)$;  
$(2)$ Solve the inequality $f(x^{2}+1) > f(10)$.

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