
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 quadratic function $f(x)=x^{2}+(2a-1)x+1-2a$,

1. Determine the truth or falsity of the proposition: "For any $a∈R$ (where $R$ is the set of real numbers), the equation $f(x)=1$ must have real roots," and write out the judgment process.
2. If $y=f(x)$ has a zero point in the intervals $(-1,0)$ and $(0, \frac {1}{2})$ respectively, find the range of the real number $a$.

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