
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 $f(x) = x^3 - \frac{1}{2}x^2 - 2x + 5$.

1. Find the monotonic intervals of $f(x)$.
2. Determine the range of values for $a$ such that three tangent lines can be drawn to $y = f(x)$ through the point $(0, a)$.

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