
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 $Q(x)$ be a polynomial such that when $Q(x)$ is divided by $x - 10$, the remainder is 150, and when $Q(x)$ is divided by $x - 50$, the remainder is 50. What is the remainder when $Q(x)$ is divided by $(x - 10)(x - 50)$?

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