
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 the function $f\left( x \right)=2{{e}^{x}}-kx-2$.

(1) Discuss the monotonicity of the function $f\left( x \right)$ in the interval $\left( 0,+\infty \right)$;

(2) If there exists a positive number $m$, such that for any $x\in \left( 0,m \right)$, the inequality $\left| f\left( x \right) \right| > 2x$ always holds, find the range of the positive real number $k$.

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