
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 $S=|x-2|+|x-4|$,  
(1) Find the minimum value of $S$;  
(2) If for any real numbers $x$, $y$, it holds that $s \geq m(-y^2+2y)$, find the maximum value of the real number $m$.

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