
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 the line $\sqrt{3}x-y+2^m=0$ is tangent to the circle $x^2+y^2=n^2$, where $n, m \in \mathbb{N}^*$, and $n-m<5$, the number of ordered pairs $(m, n)$ that satisfy the conditions is ______.

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