
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 Cartesian coordinate system $xoy$, given points $F_{1}(-1,0)$, $F_{2}(1,0)$, a moving point $P$ satisfies: $| \overrightarrow{OP}+ \overrightarrow{OF_{2}}|+| \overrightarrow{OP}- \overrightarrow{OF_{2}}|=4$.  
$(1)$ Find the equation of the trajectory $C$ of point $P$;  
$(2)$ If two parallel lines $m$, $n$ are drawn through points $(-1,0)$, $(1,0)$ respectively, and $m$, $n$ intersect the upper part of trajectory $C$ at points $A$, $B$ respectively, find the maximum value of the quadrilateral area.

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