
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
An algal cell population is found to have  $a_k$  cells on day  $k$ .  Each day, the number of cells at least doubles.  If  $a_0 \ge 1$  and  $a_3 \le 60$ , how many quadruples of integers  $(a_0, a_1, a_2, a_3)$  could represent the algal cell population size on the first  $4$  days?

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