
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 all negative \( a \) for which the equation

$$
\frac{6 \pi a-\arcsin (\sin x)+2 \arccos (\cos x)-a x}{\operatorname{tg}^{2} x+4}=0
$$

has exactly three solutions belonging to the set \( [\pi ;+\infty) \). In the answer, indicate the sum of all found \( a \) (if no such \( a \) exist, then indicate 0; if the number of \( a \) is not an integer, then round it to the nearest hundredth).

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