
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 y=f(x) on R that satisfies f(1-x)=f(x) and (x-1/2)f''(x) > 0, determine the relationship between f(x1) and f(x2) for x1 < x2 and x1 + x2 > 1.

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