
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 \(\operatorname{tg} x + \operatorname{ctg} x\) if it is known that \(\sec x - \operatorname{cosec} x = 4 \sqrt{3}\).

Recall that \(\sec x = \frac{1}{\cos x}\) and \(\operatorname{cosec} x = \frac{1}{\sin x}\).

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