
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
For any real number $x$, the notation $\lfloor x \rfloor$ represents the integer part of $x$, meaning $\lfloor x \rfloor$ is the largest integer not exceeding $x$, such as $\lfloor 2 \rfloor = 2$, $\lfloor 2.1 \rfloor = 2$, $\lfloor -2.2 \rfloor = -3$. This function $\lfloor x \rfloor$ is called the "floor function," which has a wide range of applications in mathematics itself and practical production. Given a function $f(x)$ $(x \in R)$ that satisfies $f(x) = f(2-x)$, and when $x \geq 1$, $f(x) = \log_2{x}$. Find the value of $\lfloor f(-16) \rfloor + \lfloor f(-15) \rfloor + \ldots + \lfloor f(15) \rfloor + \lfloor f(16) \rfloor$.

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