
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 that the domain of the function $f(x)= \sqrt {-x^{2}+2x+8}$ is set $A$, and the domain of the function $g(x)= \lg (-x^{2}+6x+m)$ is set $B$.

(1) When $m=-5$, find $A \cap B'$.

(2) If $A \cap B= \{x|-1 < x \leqslant 4\}$, find the value of the real number $m$.

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