
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
The function \( f(x) \) satisfies \( f\left(\frac{x}{y}\right)=f(x)-f(y) \) and \( f(x) \) is not identically zero. When \( x > 1 \), \( f(x) > 0 \). Solve the inequality: \( f(x) + f\left(x+\frac{1}{2}\right) < 0 \).

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