
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 $a$ be a real number, and the function $f(x) = -x^3 + 3x + a$.

(I) Find the monotonic intervals and extreme values of $f(x)$.

(II) If the curve $y = f(x)$ intersects the $x$-axis at exactly two points, find the value of the real number $a$.

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