
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 Cartesian coordinate system, with the non-negative half-axis of the x-axis as the initial side, if the terminal sides of angles $\alpha$ and $\beta$ intersect the unit circle at points $\left(\frac{12}{13}, \frac{5}{13}\right)$ and $\left(-\frac{3}{5}, \frac{4}{5}\right)$ respectively, then $\sin\alpha\cos\beta$ equals \_\_\_\_\_\_.

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