
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. Given the curve \\(C\\): \\(\rho = \cos \theta + \sin \theta\\), and the line \\(l\\): 
$$
\begin{cases}
x = \frac{1}{2} - \frac{\sqrt{2}}{2}t, \\
y = \frac{\sqrt{2}}{2}t
\end{cases}
$$
(where \\(t\\) is the parameter), the curve \\(C\\) intersects with the line \\(l\\) at points \\(P\\) and \\(Q\\). Find the length of the segment \\(|PQ|\\).

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