
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 lines $y = x$ and $y = \frac{x^{2}}{2^{0.1}}$ enclose a region $A$. The number of points with coordinates of the form $\left(2^{m}, 2^{n}\right)$ (where $m, n \in \mathbb{N}$) that lie inside $A$ (excluding the boundary) is ___.

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