
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
Given the function \( f(x) \) is defined on the interval \( (0,1) \), and constant \( a \) satisfies \( -\frac{1}{2}<a<\frac{1}{2} \) and \( a \neq 0 \), find the domain of the function \( F(x)=f(x+a)+f(x-a) \).

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