
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 \\(a > 0\\) and satisfies the inequality \\(2^{2a+1} > 2^{5a-2}\\).
\\((1)\\) Find the range of the real number \\(a\\).
\\((2)\\) Solve the inequality \\(\log_{a}(3x+1) < \log_{a}(7-5x)\\).
\\((3)\\) If the function \\(y=\log_{a}(2x-1)\\) has a minimum value of \\(-2\\) in the interval \\([1,3]\\), find the value of the real number \\(a\\).

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