
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 $f(x)=a^{3x+1}$, $g(x)=\left( \frac {1}{a}\right)^{5x-2}$, where $a > 0$, and $a\neq 1$.  
$(1)$ If $0 < a < 1$, find the range of values of $x$ for which $f(x) < 1$;  
$(2)$ Find the solution set of the inequality $f(x)\geqslant g(x)$ with respect to $x$.

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