
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 $\triangle ABC$ with a right angle at $C$, the median $CM$ from $C$ to the midpoint $M$ of hypotenuse $AB$ bisects the right angle into two angles of 45 degrees each. If the area of $\triangle ACM$ is $K$, find the area of $\triangle ABC$.
A) $K$
B) $2K$
C) $3K$
D) $4K$
E) $6K$

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