
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
We define \( u_{1}=17 \times(1+2) \), \( u_{2}=17^{2} \times(2+2) \), and more generally \( u_{n}=17^{n} \times(n+2) \) for any integer \( n \geqslant 1 \). Given \( a \) and \( b \) are real numbers such that \( u_{n+2}=a u_{n+1}+b u_{n} \) for all \( n \), determine \( a^{2}-b \).

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