
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 a sequence of non-negative integers $\left\{a_{n}\right\}$ that satisfies
$$
a_{1}=2016, \quad a_{n+1} \leq \sqrt{a_{n}},
$$
and if the sequence has at least 2 terms, then any two terms are distinct. How many such sequences $\left\{a_{n}\right\}$ exist?

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