
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 $f(x)=(a^{2}-a+1)x^{a+1}$ is a power function and an odd function.

(1) Find the value of $a$.
(2) Find the range of the function $g(x)=f(x)+ \sqrt {1-2f(x)}$ when $x\in [0, \frac {1}{2}]$.

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