
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 the Cartesian coordinate system, establish a polar coordinate system with the origin as the pole and the non-negative half-axis of the x-axis as the polar axis. It is known that curve $C_1: \rho=\cos\theta-\sin\theta$, and curve $$C_{2}: \begin{cases} x= \frac {1}{2}- \frac { \sqrt {2}}{2}t \\ y= \frac { \sqrt {2}}{2}t \end{cases}$$ (where $t$ is a parameter).
(1) Find the Cartesian coordinate equation of curve $C_1$;
(2) If curve $C_1$ intersects with curve $C_2$ at points P and Q, find the value of $|PQ|$.

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