
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
Let \(\{ x \}\) denote the nearest integer to \(x\), so that \(x - \frac{1}{2} \leq \{ x \} < x + \frac{1}{2}\). Define the sequence \(u_1, u_2, u_3, \ldots\) by \(u_1 = 1\) and \(u_{n+1} = u_n + \{ u_n \sqrt{2} \}\). For example, \(u_2 = 2\), \(u_3 = 5\), \(u_4 = 12\). Find the units digit of \(u_{1985}\).

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