
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 the sets be defined as follows:
$$
\begin{array}{l}
S=\left\{x \mid x^{2}-7x-30 < 0\right\}, \\
T=\left\{x \mid e^{x} > 1 - x, x \in \mathbf{Z}\right\}.
\end{array}
$$

Determine the number of non-empty proper subsets of \( S \cap T \).

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