
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
In \\(\triangle ABC\\), \\(a, b, c\\) are the sides opposite to angles \\(A, B, C\\) respectively. Given that \\(A = \frac{2\pi}{3}, b = \sqrt{2}\\), and the area of \\(\triangle ABC\\) is \\(\sqrt{3}\\), find the value of \\(a\\).

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