
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 that the vertex of angle \\(\alpha\\) coincides with the origin \\(O\\), its initial side coincides with the non-negative half-axis of the \\(x\\)-axis, and its terminal side passes through point \\(P(- \dfrac {3}{5},- \dfrac {4}{5}).\\)  
\\((\\)I\\()\\) Find the value of \\(\sin (\alpha+\pi)\\);  
\\((\\)II\\()\\) If angle \\(\beta\\) satisfies \\(\sin (\alpha+\beta)= \dfrac {5}{13}\\), find the value of \\(\cos \beta\\).

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