
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
Point \( D \) lies on side \( CB \) of right triangle \( ABC \left(\angle C = 90^{\circ} \right) \), such that \( AB = 5 \), \(\angle ADC = \arccos \frac{1}{\sqrt{10}}, DB = \frac{4 \sqrt{10}}{3} \). Find the area of triangle \( ABC \).

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