
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 that $a > 0$ and satisfies the inequality $2^{2a+1} > 2^{5a-2}$.

1. Solve the inequality $\log_{a}(3x+1) < \log_{a}(7-5x)$.
2. If the function $y = \log_{a}(2x - 1)$ has a minimum value of $-2$ in the interval $[3, 6]$, find the value of the real number $a$.

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