
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 proposition $p:|4-x|\leqslant 6$, $q:x^{2}-2x+1-a^{2}\geqslant 0\left(a \gt 0\right)$, if non-$p$ is a sufficient but not necessary condition for $q$, then the range of $a$ is ____.

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