
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
If in triangle $\triangle ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and vectors $\overrightarrow {m}=(a+c, b-a)$, $\overrightarrow {n}=(a-c, b)$, if $\overrightarrow {m} \perp \overrightarrow {n}$, then $\angle C$ equals \_\_\_\_\_\_.

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