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

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