
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 that set $A$ has $m$ elements (where $m \in \mathbf{N}^{*}$), if one element is added to $A$, the number of its subsets will increase by $\qquad$. If $k$ elements (where $k \in \mathbf{N}^{*}, k \geqslant 2)$ are added to $A$, the number of its subsets will increase by $\qquad$.

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