
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
Background: In a plane Cartesian coordinate system, given points $A(x_{1}, y_{1})$, $B(x_{2}, y_{2})$, and point $C$ is the midpoint of line segment $AB$, then the coordinates of point $C$ are ($\frac{{x}_{1}+{x}_{2}}{2}$, $\frac{{y}_{1}+{y}_{2}}{2}$). For example, if $A(-1,1)$ and $B(3,3)$, then the coordinates of the midpoint $C$ of $AB$ are ($\frac{-1+3}{2}$, $\frac{1+3}{2}$), which means the coordinates of point $C$ are (1,2).

Solving the problems:
1. Given $A(6,-2)$ and $B(-3,-3)$, then the coordinates of the midpoint $M$ of line segment $AB$ are: ______.
2. If point $P(-3,7)$ and the midpoint of line segment $PQ$ is $\left(-1,5\right)$, then the coordinates of point $Q$ are: ______.
3. Given three points $E(4,-2)$, $F(-3,-1)$, $G(-1,-4)$, and a fourth point $H(x,y)$, where the midpoint of the line segment formed by point $H$, point $E$, and point $F$ coincides with the midpoint of the line segment formed by the other two endpoints, find the coordinates of point $H$.

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