
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

We say that a number is rational if it can be written in the form $\frac{p}{q}$, with $p$ and $q$ being integers. If a real number is not rational, we say it is irrational. For example, $\frac{1}{4}$ is a rational number and $\sqrt{3}$ is irrational. Find all pairs of rational numbers $(a, b)$ such that

$$
\sqrt{a}+\sqrt{b}=\sqrt{2+\sqrt{3}}
$$

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