
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 two curves $f(x) = \cos x, g(x) = \sqrt{3}\sin x, x \in \left( 0, \frac{\pi}{2} \right)$ intersect at point $A$. If the tangents to the curves at point $A$ intersect the $x$-axis at points $B$ and $C$ respectively, then the length of segment $BC$ is.

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