
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 functions $f(x)=|x-1|$ and $g(x)=-x^{2}+6x-5$:

1. Find the range of real number $x$ values that satisfy $g(x) \geqslant f(x)$;
2. Find the maximum value of $g(x)-f(x)$.

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