
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 two sequences \( u_{1}, u_{2}, \ldots \) and \( v_{1}, v_{2}, \ldots \) with the same sequence of differences, i.e., such that \( \Delta u_{n}=\Delta v_{n} \) for all \( n \).

a) Can it be asserted that \( u_{n}=v_{n} \) ?

b) Can it be asserted that \( u_{n}=v_{n} \) if it is additionally known that \( u_{1}=v_{1}^{n} \) ?

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