
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 sequence $\{a\_n\}$ satisfies $a\_n=2a_{n-1}+2^{n}+1 (n\in\mathbb{N}^{\*},n\geqslant 2)$, with $a\_3=27$.

1. Find the values of $a\_1$ and $a\_2$.
2. If $b\_n= \frac {1}{2^{n}}(a_{n}+t)(n\in\mathbb{N}^{\*})$, find the real number $t$ such that the sequence $\{b\_n\}$ is an arithmetic progression.
3. Find the sum of the first $n$ terms, $S\_n$, of the sequence $\{a\_n\}$.

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