
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
Find all values of \(x\) for which the middle number among the three numbers

$$
a = x^{3} - 100x, \quad b = x^{4} - 16, \quad c = x + 20 - x^{2}
$$

is positive. (The middle number of the three given numbers \(a, b, c\) is called the number \(v\) in the triplet \(u \leqslant v \leqslant w\), obtained by arranging the given numbers in non-decreasing order.)

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