
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 two statements $p$ and $q$, where $p: x^2 - 8x - 20 < 0$ and $q: x^2 - 2x + 1 - a^2 \leq 0$ with $a > 0$. If the negation of $p$ ($\neg p$) is a necessary but not sufficient condition for the negation of $q$ ($\neg q$), determine the range of values for the real number $a$.

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