
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 \( \left(a_{n}\right) \) satisfies the conditions:

\[ 
a_{1}=1, \quad a_{2}=5, \quad a_{n+1}=2a_{n} - a_{n-1} \text{ for } n>1 
\]

Find the formula for the general term of the sequence.

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