
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
In triangle $\triangle ABC$, it is given that $\overrightarrow {AB}\perp \overrightarrow {AC}$, $| \overrightarrow {AB}|=3, | \overrightarrow {AC}|=4$, and point $M$ lies on segment $BC$.
(1) If $M$ is the midpoint of $BC$, find the value of $\overrightarrow {AM}\cdot \overrightarrow {BC}$.
(2) If $| \overrightarrow {AM}|= \frac {6 \sqrt {5}}{5}$, find the ratio $BM:BC$.

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