
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 \( f(x) = \begin{cases} 
\frac{1}{2}x - 1, & x \geqslant 0 \\
\frac{1}{x}, & x < 0
\end{cases} \). If \( f(a) > a \), then the range of the real number \( a \) is \(\qquad\).

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