
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
In the Cartesian coordinate system $xOy$, point $P(1,4)$ lies on the terminal side of angle $\alpha$. If ray $OP$ is rotated counterclockwise around the origin $O$ by an angle $\theta$ ($0<\theta<\pi$) to reach the terminal side of angle $\frac{3\pi}{4}$, then $\tan\theta=$ ______.

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