
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 rectangular coordinate system $(xOy)$, a polar coordinate system is established with the origin $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis. The polar coordinate equation of curve $(M)$ is given by $\sqrt{2}ρ \cos(θ + \frac{π}{4}) = 1$, and the parametric equation of curve $(N)$ is given by $\begin{cases} x = 4t^2 \\ y = 4t \end{cases}$ ($t$ is the parameter). If the curves $(M)$ and $(N)$ intersect at points $A$ and $B$, then the length of the line segment $AB$ is equal to $\_\_\_\_\_\_\_\_\_.$

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