
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
The number $a$ is such that the equation $t^{3} + 4t^{2} + 4t + a = 0$ has three real roots $x < y < z$. Determine the possible numerical values that the expression

$$
A = x^{3} - 4y^{2} - 4z^{2} - 4y - 4z + 32
$$

can take.

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