
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 vectors $\overrightarrow {a}$=(tanθ, -1) and $\overrightarrow {b}$=(1, -2), where θ is an acute angle. If the angle between $\overrightarrow {a}$+$\overrightarrow {b}$ and $\overrightarrow {a}$-$\overrightarrow {b}$ is 90°, calculate the value of $\frac {1}{2sin\theta cos\theta +cos^{2}\theta }$.

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