
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 \( A \subseteq \{1, 2, \cdots, 2014\} \), let real numbers \( \lambda_{1}, \lambda_{2}, \lambda_{3}, x_{1}, x_{2}, x_{3} \) satisfy:
(i) \( \lambda_{1}, \lambda_{2}, \lambda_{3} \in \{-1,0,1\} \) and are not all 0;
(ii) \( x_{1}, x_{2}, x_{3} \in A \);
(iii) If \( x_{i} = x_{j} \), then \( \lambda_{i} \lambda_{j} \neq -1 \) for \( 1 \leq i, j \leq 3 \).

If all numbers of the form \( x_{1} x_{2} x_{3} \) and \( \lambda_{1} x_{1} + \lambda_{2} x_{2} + \lambda_{3} x_{3} \) are not multiples of 2014, then the set \( A \) is called a "good set". Find the maximum number of elements that a good set \( A \) can contain.

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