
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 function $f(x) = \begin{cases} (2a-1)x + 4, & x \leq 1\\ a^x, & x > 1 \end{cases}$ with the domain $R$, the sequence $\{a_n\}$ $(n \in \mathbb{N}^*)$, where $a_n = f(n)$, is increasing. Determine the range of $a$.

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