
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
Consider the function $f(x)=\begin{cases} x+1 & \text{if } x\leq 0, \\ 2^{x} & \text{if } x > 0, \end{cases}$ then the range of $x$ that satisfies $f(x)+f(x-\dfrac{1}{2}) > 1$ is ___________.

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