
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
A quadratic function $f(x)$ satisfies $f(x+1)-f(x)=2x$, and $f(0)=1$.

(1) Find the expression for $f(x)$.

(2) Let $g(x)=2x+m$. If for any $x \in [-1,1]$, $f(x) > g(x)$ always holds, find the range of the real number $m$.

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