
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 $f(x)=ax^{2}+bx+c(a\neq 0)$ that satisfies $f(0)=0$, $f(x)\geqslant x$ for any $x\in R$, and $f(- \frac {1}{2}+x)=f(- \frac {1}{2}-x)$. Let $g(x)=f(x)-|\lambda x-1|(\lambda > 0)$.

1. Find the expression for the function $f(x)$;
2. Find the monotonic intervals of the function $g(x)$;
3. Investigate the number of zeros of the function $g(x)$ in the interval $(0,1)$.

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