
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 trapezoid $ABCD$, the parallel sides $AB$ and $CD$ measure 10 and 24 units, respectively, with an altitude from $A$ and $B$ to line $CD$ of 14 units. Points $G$ and $H$ are midpoints of sides $AD$ and $BC$, respectively. What are the areas of trapezoid $GHCD$ and triangle $EGH$ if $E$ is the midpoint of $GH$?

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