
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
Fill in the blank

(1) The general term of a sequence is given by _\\(a\_{n}\\)_\\(= \frac{1}{n(n+1)}\\), find the sum of the first _\\(n\\)_ terms (\\({{S}\_{n}}=\\))

(2) In triangle \\(\\triangle ABC\\), the lengths of the sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) are _\\(a\\)_, _\\(b\\)_, and _\\(c\\)_ respectively, and they satisfy the equation _\\(c\\sin A=\\)_\\(a\\cos C\\), find the maximum value of \\(\\sin A +\\)_\\(\\sin B\\)

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