
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 the function $f(x)= \frac {a\cdot 2^{x}-2}{2^{x}+1}(a∈R)$, determine the truth of the following propositions:
  1. $f(x)$ is a monotonic function on $R$;
  2. There exists an $a∈R$ such that $f(x)$ is an odd function;
  3. There exists an $a∈R$ such that $f(x)$ is an even function;
  4. When $a=1$, the sum $\sum\limits_{k=-2016}^{2016}f(k)=f(-2016)+f(-2015)+…+f(2016)$ equals a constant $(-1008)$.

Among the above propositions, the true one(s) is/are ________ (please fill in the sequence number(s) of all true propositions)

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