
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 $f(x) = \sqrt{|x+5|-|x-1|+t}$ has the domain of $\mathbb{R}$.
(1) Find the range of values for the real number $t$;
(2) If the minimum value of $t$ is $s$, and the positive real numbers $a$, $b$ satisfy $\frac{2}{a+2b} + \frac{1}{2a+b} = s$, find the minimum value of $4a+5b$.

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