
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
1. In triangle $ABC$, $A$, $B$, and $C$ are the three internal angles, and $2B = A + C$. Find the value of $tan \frac {A}{2}+tan \frac {C}{2}+ \sqrt {3}tan \frac {A}{2}tan \frac {C}{2}$.
2. Given that $sinα-cosα= \frac {1}{5}$ and $0 < α < \frac {π}{2}$, find the value of $sin(2α- \frac {π}{4})$.

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