
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
(1) Determine the range of values for $x$ satisfying the inequality $a^{2x-1} > a^{x+2}$ where $a>0$ and $a\neq 1$. Express the solution as a set.
(2) Given $f(x)$ is an odd function defined on $\mathbb{R}$, and $f(x) = \sqrt{x} + 1$ for $x > 0$, find the explicit formula for the function $f(x)$.

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