
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
Given the line $y=\frac{\sqrt{3}}{3}$ and the graphs of the functions $y=\sin x$, $y=\cos x$, and $y=\tan x$ within the interval $({0,\frac{\pi}{2}})$, find the value of $\cos (x_{1}+x_{2}+x_{3})$.

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