
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 in \\(\triangle ABC\\), the sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) are \\(a\\), \\(b\\), and \\(c\\) respectively, and \\(A=2C\\).

  

\\((1)\\) If \\(\triangle ABC\\) is an acute triangle, find the range of values for \\(\dfrac{a}{c}\\);

\\((2)\\) If \\(b=1\\) and \\(c=3\\), find the area of \\(\triangle ABC\\).

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