
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 $θ∈(-\frac{π}{2},0)$, and $cos2θ-3sin(θ-\frac{π}{2})=1$, determine the value of $tan(\frac{π}{4}-θ)$.

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