
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 $f$ be a mapping from point set $A$ to point set $B$, such that for any $(x,y) \in A$, we have $f(x,y) = (y-x, y+x)$. Given a sequence of points in set $A$, $P_n(a_n, b_n)$ where $n \in \mathbb{N^{*}}$, and $P_{n+1}(a_{n+1}, b_{n+1}) = f(a_n, b_n)$ for each $n$. The point $P_1$ is given by $(0,2)$. Find the length of the line segment $\overline{P_{2013}P_{2014}}$.

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