
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 the right triangle \( \triangle ABC \) with right angle at \( C \), the altitude \( CH \) and the median \( CM \) trisect the right angle, calculate the area of \( \triangle ABC \) given that the area of \( \triangle CHM \) is \( k \).

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