
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 $\cos (75^{\circ}+\alpha)= \frac {5}{13}$, where $\alpha$ is an angle in the third quadrant,  
(1) Find the value of $\sin (75^{\circ}+\alpha)$.  
(2) Find the value of $\cos (\alpha-15^{\circ})$.  
(3) Find the value of $\sin (195^{\circ}-\alpha)+\cos (105^{\circ}-\alpha)$.

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