
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 $f(x)= \sqrt {|x+3|-|x-1|+5}$.
(1) Find the range of the function $f(x)$;
(2) If the range of the function $f(x)$ is $[m,n]$, and $a^{2}+b^{2}=m$, $c^{2}+d^{2}=n$, find the range of $ac+bd$.

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