
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 set $A$ is the domain of the function $y=\lg(6+5x-x^2)$, and set $B$ is the solution set of the inequality $x^2-2x+1-a^2\geqslant 0$ $(a > 0)$. Let $p$: $x \in A$, $q$: $x \in B$.
$(1)$ If $A \cap B = \varnothing$, find the range of $a$;
$(2)$ If $\neg p$ is a sufficient but not necessary condition for $q$, find the range of $a$.

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