
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 $f(x) = \begin{cases} (2a-1)x+3a, & x<1 \\ a^{x}, & x\geq 1 \end{cases}$, it satisfies that for any $x_1 \neq x_2$, the inequality $(x_1-x_2) \cdot (f(x_1)-f(x_2)) < 0$ holds. Determine the range of values for $a$.

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