
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
A rectangle has length $AC = 40$, and width $AE = 30$. Point $B$ is located one-third the distance from $A$ to $C$ along segment $\overline{AC}$, and $F$ is the midpoint of $\overline{AE}$. An equilateral triangle $CEF$ is added outside the rectangle, sharing segment $\overline{EF}$ as one of its sides. Calculate the area of the shape composed of rectangle $ACDE$ plus triangle $CEF$ minus triangle $ABF$.

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