
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 $\overrightarrow {a}=(5,-12)$ and $\overrightarrow {b}=(-3,4)$.

(1) Find the cosine value of the angle $\theta$ between $\overrightarrow {a}$ and $\overrightarrow {b}$.

(2) If the vector $\overrightarrow {a}+t\overrightarrow {b}$ is perpendicular to $\overrightarrow {a}-\overrightarrow {b}$, find the value of the real number $t$.

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