
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
Given the area of \\(\triangle ABC\\) is \\(S\\), and \\(\overrightarrow{AB} \cdot \overrightarrow{AC} = S\\).

\\((1)\\) Find the value of \\(\tan A\\);

\\((2)\\) If \\(B = \frac{\pi}{4}\\) and \\(c = 3\\), find the area \\(S\\) of \\(\triangle ABC\\).

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