
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 the arithmetic sequence $\{a_n\}$ with first term $a_1=2$ and common difference $d=1$, and the geometric sequence $\{b_n\}$ with first term $b_1=1$ and common ratio $q=2$. If the sequence $\{M_n\}$ satisfies $M_n=a_{b_1}+a_{b_2}+a_{b_3}+...+a_{b_n}$, find the number of terms in the sequence $\{M_n\}$ that are less than 2016.

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