
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
Let $f(x)$ be a function defined on $\mathbb{R}$. Given that $f(0)=2016$ and for all $x \in \mathbb{R}$, it satisfies $f(x+2) - f(x) \leq 3 \cdot 2^x$ and $f(x+6) - f(x) \geq 63 \cdot 2^x$. Find the value of $f(2016)$.

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