
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 sum of its first $n$ terms being $S_n$, if $a_1$ is the maximum value of the function $f(x)= \sqrt{3}\sin x + \cos x$ where $x \in \mathbb{R}$, and it satisfies $a_n - a_nS_{n+1} = \frac{a_1}{2} - a_nS_n$, then the product of the first $2018$ terms of the sequence $\{a_n\}$, denoted as $A_{2018}$, calculate its value.

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