
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 $f(x) = -x^3 + ax^2 + 1$ $(a \in \mathbb{R})$.  
(1) If the function $y = f(x)$ is increasing in the interval $(0, \frac{2}{3})$ and decreasing in the interval $[\frac{2}{3}, +\infty)$, find the value of $a$;  

(2) When $x \in [0,1]$, let the slope angle of the tangent line at any point on the graph of the function $y = f(x)$ be $\theta$. If a constant $a \in (\frac{2}{3}, +\infty)$ is given, find the range of values for $\tan \theta$.

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