
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
Determine the range of values for $x$ such that the function $f(x)$ satisfies the inequality $f(x) + f\left(x-\frac{1}{2}\right) > 1$, where $f(x)$ is defined as:
$$
f(x)=\begin{cases}
x + 1 & \text{if } x \leq 0, \\
2^x & \text{if } x > 0.
\end{cases}
$$

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