
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
For a sequence $\{x_n\}$, we say it is a "diminishing difference sequence" if for any $n \in \mathbb{N}^*$ the inequality $\frac {x_{n}+x_{n+2}}{2} < x_{n+1}$ holds. Suppose the sequence $\{a_n\}$ is a geometric sequence whose terms are all positive, let $S_n$ be the sum of its first $n$ terms, and suppose $a_1 = 1$, $S_3 = \frac {7}{4}$.  
(1) Find the general term formula for the sequence $\{a_n\}$ and determine whether the sequence $\{S_n\}$ is a "diminishing difference sequence";  
(2) Let $b_n = (2 - na_n)t + a_n$, if the sequence $b_3, b_4, b_5, \ldots$ is a "diminishing difference sequence", determine the range of the real number $t$.

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