
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
If the solution set of the inequality $|2x+5|+|2x-1|-t\geq0$ with respect to $x$ is $\mathbb{R}$,  
(1) find the maximum value $s$ of the real number $t$;  
(2) if the positive real numbers $a$ and $b$ satisfy $4a+5b=s$, find the minimum value of $y= \frac {1}{a+2b}+ \frac {4}{3a+3b}$.

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