
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
Let $a \in \mathbb{R}$, the quadratic equation in $x$, $7x^2 - (a+13)x + a^2 - a - 2 = 0$ has two real roots $x_1$, $x_2$, and $0 < x_1 < 1 < x_2 < 2$.

(1) Find the range of values for $a$;
(2) Compare the magnitude of $a^3$ with $a^2 - a + 1$.

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