
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
The sum of the first $n$ terms of the sequence $\{a_n\}$ is denoted as $S_n$, and $a_1=t$. The point $(S_n, a_{n+1})$ lies on the line $y=2x+1$, where $n \in \mathbb{N}^*$. If the sequence $\{a_n\}$ is a geometric sequence, then the real number $t=$ $\boxed{1}$.

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