
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
Find the numerical value of
\[
\frac{2\sin 30^\circ \cos 10^\circ + 3\cos 150^\circ \cos 110^\circ}{4\sin 40^\circ \cos 20^\circ + 5\cos 140^\circ \cos 100^\circ}.
\]

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