
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 $f(x)=\frac{{-{2^x}+a}}{{{2^{x+1}}+2}}$ be an odd function with domain $R$. <br/>$(1)$ Find the value of the real number $a$; <br/>$(2)$ If there exists $θ∈[{-\frac{π}{4},0}]$ such that $f(\sqrt{3}\sinθ\cosθ)+f(k-{\cos^2}θ)>0$, find the range of the real number $k$.

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