
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: In the sequence $\{a_n\}$, $a_1=1$, $a_{n+1}= \frac {a_n}{3a_n+1}$, determine the monotonicity of $\{a_n\}$.  
Xiao Ming provided the following solution approach, please complete the solution process.  
Step 1, Calculation:  
Based on the given conditions, calculate: $a_2=$ ______ , $a_3=$ ______ , $a_4=$ ______ .  
Step 2, Conjecture:  
The sequence $\{a_n\}$ is a ______ (fill in increasing or decreasing) sequence.  
Step 3, Proof:  
Since $a_{n+1}= \frac {a_n}{3a_n+1}$, so $ \frac {1}{a_{n+1}}= \frac {3a_n+1}{a_n}= \frac {1}{a_n}+$ ______ .  
Therefore, it can be judged that the sequence $\{ \frac {1}{a_n}\}$ is an arithmetic sequence with the first term $\frac {1}{a_1}=$ ______ , and common difference $d=$ ______ .  
Hence, the general formula for the sequence $\{ \frac {1}{a_n}\}$ is ______ .  
And from this, it can be judged that:  
The sequence $\{ \frac {1}{a_n}\}$ is a ______ (fill in increasing or decreasing) sequence, and each term is ______ (fill in positive, negative, or zero).  
Therefore, the sequence $\{a_n\}$ is a ______ (fill in increasing or decreasing) sequence.

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