
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
Find the constants $\alpha$ and $\beta$ such that the equation $\frac{x-\alpha}{x+\beta} = \frac{x^2 + 120x + 1575}{x^2 - 144x + 1050}$ holds true for all $x$ where the expressions are defined. What is $\alpha + \beta$?

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