
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
Let the vertex of angle $\theta$ be the origin of the coordinates, and the initial side be the non-negative half-axis of the $x$-axis. Establish a Cartesian coordinate system in the plane. If the terminal side of angle $\theta$ passes through point $P(1,2)$, then $tan(\theta+\frac{π}{4})=$____.

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