
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
Let \(a\) and \(b\) be real numbers such that \(\frac{\sin a}{\sin b} = 2\) and \(\frac{\cos a}{\cos b} = 3\). Find the value of
\[
\frac{\sin 3a}{\sin 3b} + \frac{\cos 3a}{\cos 3b}.
\]

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