
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 \\( \triangle ABC \\), with angles \\( A \\), \\( B \\), and \\( C \\) opposite to sides \\( a \\), \\( b \\), and \\( c \\) respectively, it is given that \\( b\tan A = (2c - b) \tan B \\).
\\((1)\\) Find angle \\( A \\);
\\((2)\\) If \\( a = \sqrt{13} \\) and \\( b = 3 \\), find the area of \\( \triangle ABC \\).

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