
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
To ensure the water supply for a fruit planting base, an irrigation canal needs to be built. It is planned to build an irrigation canal of $1650$ meters, to be completed by two construction teams, Team A and Team B, working together. Team B builds $30$ meters more per day than Team A. The number of days Team A alone needs to complete the construction task is $\frac{3}{2}$ times the number of days Team B alone needs.<br/>$(1)$ Find out how many meters each team builds per day;<br/>$(2)$ Given that the daily construction cost for Team A is $90,000$ yuan and for Team B is $120,000 yuan, if Team A works alone for a certain number of days before Team A and Team B work together and complete the construction task in exactly $14$ days, find out the total construction cost in yuan.

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