
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 a moving point P whose distance to the line $x=4$ is twice the distance to the fixed point $F_1(1,0)$,  
(1) Find the equation of the trajectory of point P;  
(2) A line passing through $F_1$ with a slope of $k=1$ intersects the trajectory at points C and D. If $A(2,0)$, find the area $S$ of $\triangle ACD$.

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