
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]


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Given an odd function f(x) defined on ℝ, let its derivative be f′(x). When x ∈ (−∞,0], it always holds that xf′(x) < f(−x). Let F(x) = xf(x), then determine the range of real numbers x that satisfy F(3) > F(2x-1).

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