
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 that $\{a\_n\}$ is an increasing arithmetic sequence satisfying $a\_2a\_4=21$ and $a\_1+a\_5=10$.

1. Find the general term formula for $\{a\_n\}$.
2. If the sequence $\{c\_n\}$ has the sum of its first $n$ terms equal to $C\_n=a\_n+1$, and the sequence $\{b\_n\}$ satisfies $b\_n=2^{n}c\_n\ (n∈N^{})$, find the sum of the first $n$ terms of $\{b\_n\}$.

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