
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 $\overrightarrow {AB} = (3, 1)$, $\overrightarrow {AC} = (-1, a)$, where $a \in \mathbb{R}$  
(1) If D is the midpoint of BC, and $\overrightarrow {AD} = (m, 2)$, find the values of $a$ and $m$;  
(2) If $\triangle ABC$ is a right-angled triangle, find the value of $a$.

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