
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 $\triangle ABC$, let $a$, $b$, and $c$ be the sides opposite to angles $A$, $B$, and $C$, respectively. Denote the area of $\triangle ABC$ as $S$, and assume $$2S= \overrightarrow {AB}\cdot \overrightarrow {AC}$$.
(1) Find the measure of angle $A$;
(2) If $c=7$ and $$\cos B= \frac {4}{5}$$, find the value of $a$.

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