
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 that $\cos\theta= \frac {4}{5}$, where $\theta\in(0, \frac {\pi}{2})$,
(Ⅰ) find the value of $\sin 2\theta$;
(Ⅱ) find the value of $\cos\left(\theta+ \frac {\pi}{4}\right)$;
(Ⅲ) find the value of $\tan\left(\theta+ \frac {\pi}{4}\right)$.

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