
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 the function $f(x)=\lg (x+m)$ where $m\in\mathbb{R}$;  
$(1)$ When $m=2$, solve the inequality $f\left( \dfrac {1}{x}\right) > 1$;  
$(2)$ If $f(0)=1$, and $f(x)=\left( \dfrac {1}{ \sqrt {2}}\right)^{x}+\lambda$ has a real solution in the closed interval $[2,3]$, find the range of the real number $\lambda$;  
$(3)$ If the graph of the function $f(x)$ passes through the point $(98,2)$, and the inequality $f[\cos (2^{n}x)] < \lg 2$ holds for any $n\in\mathbb{N}$, find the set of values for the real number $x$.

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