
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 function $y=x^3+3x^2+x$, there exists a certain point $P$ on the graph $C$ such that: if a line $l$ passing through point $P$ intersects the curve $C$ at two points $M(x_1, y_1)$ and $N(x_2, y_2)$ different from $P$, then $y_1+y_2$ always equals a constant value $y$. Find the value of $y$.

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