
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
For the sequence of numbers \( n_{1}, n_{2}, n_{3}, \ldots \), the relation \( n_{i} = 2 n_{i-1} + a \) holds for all \( i > 1 \). If \( n_{2} = 5 \) and \( n_{8} = 257 \), what is \( n_{5} \)?

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