
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
In a Cartesian coordinate system, the "rectangular distance" between points $P\left(x_{1}, y_{1}\right)$ and $Q\left(x_{2}, y_{2}\right)$ is defined as $d(P, Q) = \left|x_{1}-x_{2}\right| + \left|y_{1}-y_{2}\right|$. If the "rectangular distance" from point $C(x, y)$ to points $A(1,3)$ and $B(6,9)$ is equal, where real numbers $x$ and $y$ satisfy $0 \leq x \leq 10$ and $0 \leq y \leq 10$, then the total length of the trajectory of all points $C$ that satisfy the condition is .

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