
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 set $M$ consisting of all functions $f(x)$ that satisfy the property: there exist real numbers $a$ and $k$ ($k \neq 0$) such that for all $x$ in the domain of $f$, $f(a+x) = kf(a-x)$. The pair $(a,k)$ is referred to as the "companion pair" of the function $f(x)$.

1. Determine whether the function $f(x) = x^2$ belongs to set $M$ and explain your reasoning.
2. If $f(x) = \sin x \in M$, find all companion pairs $(a,k)$ for the function $f(x)$.
3. If $(1,1)$ and $(2,-1)$ are both companion pairs of the function $f(x)$, where $f(x) = \cos(\frac{\pi}{2}x)$ for $1 \leq x < 2$ and $f(x) = 0$ for $x=2$. Find all zeros of the function $y=f(x)$ when $2014 \leq x \leq 2016$.

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