
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 the domain of the function $f(x)$, defined on $R$, is an odd function. When $x \gt 0$, $f(x)=\frac{x}{3}-{2^x}$.  
$(1)$ Find the analytical expression of $f(x)$.  
$(2)$ If for any $t\in R$, the inequality $f(t^{2}-2t)+f(2t^{2}-k) \lt 0$ always holds, find the range of real number $k$.

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