
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  $n$  be an integer, and let  $\triangle ABC$  be a right-angles triangle with right angle at  $C$ . It is given that  $\sin A$  and  $\sin B$  are the roots of the quadratic equation \[(5n+8)x^2-(7n-20)x+120=0.\] Find the value of  $n$ 

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