
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 $f(x)=\begin{cases} 
x+1, & \text{if } x\leqslant 0 \\
2^{x}, & \text{if } x > 0 \\
\end{cases}$, then the range of $x$ that satisfies $f(x)+f\left(x-\frac{1}{2}\right) > 1$ is        .

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