
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 a large square plot of land, two small triangular gardens are formed as follows: Triangle $ABC$ is right-angled at $B$, $\angle B = 90^\circ$, with $AB = BC$. Triangle $DEF$ is also right-angled at $E$, with $DE = EF = 8\sqrt{2}$. Calculate the total area of the triangles $ABC$ and $DEF$ if $AB = 12$.

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