
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 $\triangle ABC$, the side lengths opposite to the angles $\angle A$, $\angle B$, and $\angle C$ are $a$, $b$, and $c$ respectively, and it is given that
$$
\begin{array}{l}
\sin C \cdot \cos \frac{A}{2}=(2-\cos C) \sin \frac{A}{2}, \\
\cos A=\frac{3}{5}, \quad a=4.
\end{array}
$$

Then the area of $\triangle ABC$ is ___.

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