
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
Regarding the function $f(x)=\cos (2x- \frac {π}{3})+\cos (2x+ \frac {π}{6})$, determine the correctness of the following propositions:

1. The maximum value of $y=f(x)$ is $\sqrt {2}$;
2. $y=f(x)$ is an even function on its domain;
3. $y=f(x)$ is a decreasing function on the interval $[\frac {π}{24}, \frac {13π}{24}]$;
4. Translating the graph of the function $y= \sqrt {2}\cos 2x$ to the right by $\frac {π}{24}$ units will coincide with the graph of $y=f(x)$.

Provide the sequence number(s) of the correct proposition(s).

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