
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 a sequence $\{a_{n}\}$ with the general term $a_{n}= \frac {n}{n+a}$ ($n, a \in \mathbb{N}^{*}$).

(1) If $a_{1}$, $a_{3}$, $a_{15}$ form a geometric sequence, find the value of $a$;  
(2) When $k$ ($k \geq 3$ and $k \in \mathbb{N}^{*}$), $a_{1}$, $a_{2}$, $a_{k}$ form an arithmetic sequence, find the value of $a$.

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