
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

If the real numbers \(a, b, c\) are arranged in non-decreasing order resulting in the triplet \(x_{1} \leqslant x_{2} \leqslant x_{3}\), then the number \(x_{2}\) is called the median of the numbers \(a, b, c\). Find all values of \(t\) at which the median of the three numbers

$$
a=t^{3}-100t ; \quad b=2^{t}-16 ; \quad c=\sin t - \frac{1}{2}
$$

is positive.

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