
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
Given the parametric equations for line $l$ as follows:
$$
\begin{cases}
x = 2t, \\
y = 1 + bt
\end{cases}
$$
where $t$ is the parameter, and in the polar coordinate system with the origin as the pole and the positive x-axis as the polar axis, the equation of curve $C$ is $\rho = 2\cos\theta$. If line $l$ bisects the area enclosed by curve $C$, then find the value of $b$.

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