
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 the function $f(x) = x^3 - 2x^2 + ax \ (x \in \mathbb{R}, a \in \mathbb{R})$, there is exactly one tangent line $l$ to the curve $y = f(x)$ that is perpendicular to the line $y = x$.

(1) Determine the value of $a$ and the equation of the tangent line $l$;

(2) Let the angle of inclination of the tangent line at any point on the curve $y = f(x)$ be $\theta$. Find the range of values for $\theta$.

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