
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 an odd function $f\left(x\right)$ defined on the set of real numbers $R$, and $f\left(x\right)$ is a decreasing function on $\left(-\infty ,+\infty \right)$, is there a real number $m$ such that $f\left(4m-2m\cos \theta \right)+f(2\cos ^{2}\theta -4) \gt f\left(0\right)$ holds for all $θ∈[{-\frac{π}{3},\frac{π}{2}}]$? If it exists, find the range of real numbers $m$ that satisfy the condition; if it does not exist, explain the reason.

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