
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
Let \\(x\\), \\(y \in \mathbb{R}\\), \\(a > 1\\), \\(b > 1\\). If \\(a^{x} = b^{y} = 3\\) and \\(a + b = 2\sqrt{3}\\), then the maximum value of \\(\dfrac{1}{x} + \dfrac{1}{y}\\) is \_\_\_\_\_.

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