
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 that  $\left(u_n\right)$  is a sequence of real numbers satisfying  $ u_{n \plus{} 2} \equal{} 2u_{n \plus{} 1} \plus{} u_{n}$ , and that  $ u_3 \equal{} 9$  and  $ u_6 \equal{} 128$ . Determine the value of $ u_5$.

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