
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 that the distance from a moving point $P$ to the $y$-axis is less than its distance to the point $M(-1, 0)$ by $1$.

(I) Find the trajectory equation of the moving point $P$;

(II) If the line $l: x + y + 1 = 0$ intersects with the trajectory of the moving point $P$ at points $A$ and $B$, find the area of $\triangle OAB$.

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