
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  $a_0 = 1$  and define the sequence  $\{a_n\}$  by \[a_{n+1} = \frac{\sqrt{3}a_n - 1}{a_n + \sqrt{3}}.\] If  $a_{2017}$  can be expressed in the form  $a+b\sqrt{c}$  in simplest radical form, compute  $a+b+c$ .

*2016 CCA Math Bonanza Lightning #3.2*

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