
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 the sequence $\{a\_n\}$ that satisfies the recurrence relation $a\_n=2a_{n-1}+1$, $(n\geqslant 2)$, where $a\_4=15$
(1) Find $a\_1$, $a\_2$, $a\_3$
(2) Find the general term formula for the sequence $\{a\_n\}$
(3) Find the sum $S$ of the first $n$ terms of the sequence $\{a\_n\}$

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