
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 $a\_1=1$, $a\_{n+1}=2a\_n+1 (n∈N^∗).$

(1) Find $a\_2$, $a\_3$, $a\_4$, $a\_5$;

(2) Inductively guess the general term formula $a\_n$.

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