
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
For positive numbers $x$ and $y$, define the operation $\heartsuit(x, y)$ as
\[
\heartsuit(x, y) = x - \sqrt{\frac{1}{y}}
\]
Calculate $\heartsuit(3, \heartsuit(3, 3))$.
A) $\frac{26}{9}$
B) $\frac{27-\sqrt{3(9+\sqrt{3})}}{9}$
C) $\frac{28}{9}$
D) $\frac{29}{9}$

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