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