
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 a sequence $\left(u_{n}\right)$ with the first term $u_{0}$ and for any natural number $n$:

$$
u_{n+1}=a u_{n}+b
$$

Express the $n^\text{th}$ term of the sequence in terms of $u_{0}$.

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