
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 $f\left( x \right)=\frac{{{e}^{x}}-a}{{{e}^{x}}+1}\left( a\in R \right)$ defined on $R$ as an odd function.

(1) Find the range of the function $y=f\left( x \right)$;

(2) When ${{x}_{1}},{{x}_{2}}\in \left[ \ln \frac{1}{2},\ln 2 \right]$, the inequality $\left| \frac{f\left( {{x}_{1}} \right)+f\left( {{x}_{2}} \right)}{{{x}_{1}}+{{x}_{2}}} \right| < \lambda \left( \lambda \in R \right)$ always holds. Find the minimum value of the real number $\lambda$.

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