
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
From a point \( M \), located inside triangle \( ABC \), perpendiculars are drawn to sides \( BC \), \( AC \), and \( AB \), with lengths \( k \), \( l \), and \( m \) respectively. Find the area of triangle \( ABC \), given that \(\angle CAB = \alpha\) and \(\angle ABC = \beta\). If the answer is not an integer, round it to the nearest whole number.

$$
\alpha = \frac{\pi}{6}, \beta = \frac{\pi}{4}, k = 3, l = 2, m = 4
$$

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