
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 $C$, altitude $CH$, and median $CM$ are such that $\angle MCB = 45^\circ$, $CM$ is the median of hypotenuse $AB$, and $CH$ is the perpendicular from $C$ to $AB$. If the area of $\triangle CHM$ is $K$, then the area of $\triangle ABC$ is?
A) $2\sqrt{2} K$
B) $4\sqrt{2} K$
C) $3K$
D) $4K$
E) $6K$

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