
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
It is possible to express the sum  $$ \sum_{n=1}^{24}\frac{1}{\sqrt{n+\sqrt{n^2-1}}} $$  as  $a\sqrt{2}+b\sqrt{3}$ , for some integers  $a$  and  $b$ . Compute the ordered pair  $(a,b)$ .

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