
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
(Science) If acute angles $α$ and $β$ satisfy $\tan α \cdot \tan β= \frac {13}{7}$, and $\sin (α-β)= \frac { \sqrt {5}}{3}$, find:  
(1) $\cos (α-β)$; (2) $\cos (α+β)$

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