
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

Calculate (without using a table) the value of the following expression:

$$
\operatorname{tg} \frac{\pi}{8}+\operatorname{ctg} \frac{\pi}{8}+\operatorname{tg} \frac{\pi}{16}-\operatorname{ctg} \frac{\pi}{16}+\operatorname{tg} \frac{\pi}{24}+\operatorname{ctg} \frac{\pi}{24}
$$

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