
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 \( n \) (\( n \geq 3 \)) real numbers \( a_1, a_2, \cdots, a_n \) such that \( a_1 = 1 \), \( a_n = 1 \), and \( |a_{i+1} - a_i| \leq 2 \) for \( 1 \leq i \leq n-1 \), calculate the smallest value of the positive integer \( n \) such that \( a_1 + a_2 + \cdots + a_n = 2016 \).

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